Abstract:

Superconducting qubits that operate at microwave frequencies are one of the most promising platforms for quantum information processing. However, connecting distant processors with microwave photons is challenging since microwave photons suffer from thermal noise and large propagation losses in room temperature components.

Conversely, optical photons within the telecommunications band are known to have extremely low loss in optical fiber and the thermal noise is minuscule at room temperature. In order to interface superconducting qubits with room temperature optical photons, a quantum transducer is required that can convert photons between microwave and optical frequencies.

This thesis describes the development of a microwave-to-optical transducer using an ensemble of erbium ions, doped within a yttrium orthovanadate crystal, that are simultaneously coupled to a superconducting microwave resonator and a photonic crystal optical resonator. The erbium ions have spin transitions that couple to the microwave resonator and optical transitions at telecom wavelengths that couple to the optical resonator.

ID: CaltechTHESIS:05152022-181826611

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Abstract:

Achieving an efficient interface of light and matter has been a principal goal in the field of quantum optics. A burgeoning paradigm in the study of light-matter interface is waveguide quantum electrodynamics (QED), where quantum emitters are coupled to a common one-dimensional waveguide channel. In this scenario, cooperative effects among quantum emitters emerge as a result of real and virtual exchange of photons, giving rise to new ways of controlling matter.

Superconducting quantum circuits offer an exciting platform to study quantum optics in the microwave domain with artificial quantum emitters interfaced to engineered photonic structures on chip. Beyond revisiting the experiments performed in atom-based platforms, superconducting circuits enable exploration of novel regimes in quantum optics that are otherwise prohibitively challenging to achieve. Moreover, the unprecedented level of control over individual quantum degrees of freedom and good scalability of the system provided by state-of-the-art circuit QED toolbox set a promising direction towards the study of quantum many-body phenomena.

In this thesis, I discuss waveguide QED experiments performed in superconducting quantum circuits where transmon qubits are coupled to engineered microwave waveguides. Employing the high flexibility and controllability of superconducting quantum circuits, we realize and explore various schemes for generating waveguide-mediated interactions between superconducting qubits. We also demonstrate an intermediate-scale quantum processor based on a dispersive waveguide QED system involving ten superconducting qubits, exploring quantum many-body dynamics in a highly controllable fashion. The work described in the thesis marks an important step towards the construction of scalable architectures for quantum simulation of many-body models and realization of efficient coupling schemes for quantum computation.

ID: CaltechTHESIS:02122022-205429202

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Abstract:

In this thesis, we take a look at how quantum information theory can be used to study physical systems at both high and low energies.

In the first part of this thesis, we examine the structure of the low-energy subspaces of quantum many-body systems. We show that the existence of error-correcting properties in low-energy subspaces is a generic feature of quantum systems. Using the formalism of matrix product states, we construct explicit quantum error-detecting codes formed from the momentum eigenstates of a quantum many-body system.

We also examine how topological order can persist past the ground state space into the low-energy subspace of excited states by studying the No Low-Energy Trivial States (NLTS) conjecture. We prove a version of the NLTS conjecture under the assumption of symmetry protection. Moreover, we show that our symmetric NLTS result has implications for the performance of quantum variational optimization algorithms by using it to prove a bound on the Quantum Approximate Optimization Algorithm (QAOA).

In the second part of this thesis, we examine problems related to bulk reconstruction in holography and the black hole firewall paradox. Using the formalism of the tensor Radon transform, we devise and implement a numerical algorithm for reconstructing (perturbatively in AdS₃/CFT₂) the bulk metric tensor from a given boundary entropy profile.

We finally examine the black hole firewall problem from the perspective of quantum error-correction and quantum computational complexity. We argue that the state of the Hawking radiation has the special property of being computationally pseudorandom, meaning that it cannot be distinguished from the maximally mixed state by any efficient quantum computation. We show that this implies that each black hole has a natural structure as a quantum error-correcting code.

ID: CaltechTHESIS:05182021-042001387

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Abstract:

A closed quantum system never forgets its initial state, but the encoded information can get scrambled and become inaccessible without measuring a large fraction of all the system degrees of freedom. This scrambling can be diagnosed by studying the spatial spreading of initially local operators under the Heisenberg time evolution, and the decay of the out-of-time-ordered correlators (OTOC). What insights can OTOCs provide to understand the dynamics of quantum many-body systems? What are the characteristic behaviors of OTOCs during the time evolution? How is information scrambling affected by the dissipation in open quantum many-body systems?

We first study slow scrambling in many-body localized systems via calculating various correlators, two-point retarded correlators and OTOCs. Comparing with retarded correlators, OTOCs provide more information about the dynamics. We find that disorder slows and partially halts the onset of information scrambling. Instead of ballistic spreading, propagation of information forms a logarithmic light cone.

Next, we study the finite-size scaling of OTOCs at late times in generic thermalizing quantum many-body systems. When energy is conserved, the late-time saturation value of the OTOC of generic traceless local operators scales as an inverse polynomial in the system size. This is in contrast to the inverse exponential scaling expected for chaotic dynamics without energy conservation.

We also study information scrambling in open quantum many-body systems. We define a dissipative version of OTOC and study its behaviors in a prototypical chaotic quantum chain with dissipation. We find that dissipation leads to not only the overall decay of the scrambled information due to leaking, but also structural changes so that the information light cone can only reach a finite distance even when the effect of overall decay is removed.

Finally, we construct a family of local Hamiltonians for understanding the asymmetric information scrambling. Our models live on a one-dimensional lattice and exhibit asymmetric butterfly light cone between the left and right spatial directions.

ID: CaltechTHESIS:02262020-182938837

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Abstract:

Due to its high coherence in transmission over a large distance in the ambient environment, the quantum optical system has been a prevailing platform for long-distance quantum communication, which was recently realized over a continental distance with a low earth orbit satellite and ground stations [102, 70]. However, the pure quantum optical system has so far shown weak interactions between photon and matter, which makes it inefficient in carrying out deterministic quantum gates for quantum repeater based scalable quantum network and quantum computing. On the other hand, superconducting quantum systems operating in the microwave domain with Josephson junction transmon qubits have proven to be capable of efficient deterministic quantum operations on quantum states [86, 87, 66]. Nevertheless, such architecture is prone to errors and decoherence due to cross-talk between microwave elements in a large-scale superconducting quantum circuit. Furthermore, superconducting systems, in general, also have large footprint (100s um) elements (resonators and superconducting quantum bits) [92, 60] that limit the ability to scale up a superconducting quantum system. Moreover, microwave quantum circuits require cooling to around 10 mK, making it unsuitable for communicating quantum information outside a dilution refrigerator (DF). Micro- and nano- acoustic elements have been extensively used in conventional integrated information processing systems due to their compactness and high coherence [97]. Acoustic systems in quantum engineering also have the advantage of being a platform for universal couplings between various quantum systems including spins, optical photons, and superconducting circuits. As it will be discussed in this thesis, elements critical to scalable optical quantum network and superconducting quantum circuit can be constructed relying on the cavity optomechanics and piezoelectric interactions.

Optomechanical interaction is concerned with the light pressure coupling of cavity mechanical deformation to a strong optical ﬁeld. This interaction has allowed the close to mechanical ground state cooling of mechanical resonators using laser and the ultra-sensitive displacement measurement that led to the detection of gravitational waves in the LIGO collaboration [125, 25]. Optomechanical crystals (OMCs) are lithographically patterned devices which contain a periodic structure that host bandgaps for both optical band electromagnetic waves and microwave band acoustic waves. A properly engineered defect in the crystal can conﬁne and localize acoustic and electromagnetic modes of similar wavelengths into a small mode volume [17, 20, 21]. A strong optomechanical coupling, which can be achieved between such strongly conﬁned co-localized optical and acoustic modes, can be used in engineering the quantum state of mechanical motion to realize useful quantum devices such as a high-coherence quantum memory [74] and an optomechanical high efficiency optical isolator for unidirectionally connecting distant optical cavities via an acoustic bus [37].

To strongly couple the mechanical degree of freedom with a superconducting quantum circuit, various methods can be used, ranging from electromechanic coupling (electric coupling to a mechanically compliant capacitor), magnetomechanical coupling (magnetic coupling to a vibrating SQUID loop), and piezoelectric coupling. The recent advent of quantum acoustics [23, 8, 9] was realized with the strong piezoelectric coupling between a superconducting transmon qubit and a high-coherence mechanical resonator. The engineered strong piezoacoustic coupling provides the possibility to carry out deterministic ultra-high ﬁdelity two-qubit quantum gates on non-classical mechanical quantum states [52]. This ability together with the recent demonstration of ultra-long phonon lifetime mechanical resonators show the possibility of integrating the ultra-high quality mechanical resonator as a compact quantum memory element and even a new ultra-compact (10s um) quantum bit architecture for scalable superconducting quantum circuits. Furthermore, the strong piezoelectric coupling that can transduce quantum state in a superconducting circuit into mechanical wave also makes it possible to efficiently transduce a quantum state between a superconducting quantum circuit and a telecommunication band optical channel via a mechanical waveguide connected to an optomechanical crystal cavity.

ID: CaltechTHESIS:08282019-141610693

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Abstract:

This thesis presents on-chip quantum storage of telecommunication wavelength light using nanophotonic resonators coupled to erbium ions. Storage of light in an optical quantum memory has applications in quantum information and quantum communication. For example, long distance quantum communication using quantum repeater protocols is enabled by quantum memories. Efficient and broadband quantum memories can be made from resonators coupled to ensembles of atoms. Like other rare earth ions, erbium is appealing for quantum applications due to its long optical and hyperfine coherence times in the solid state at low temperatures. However, erbium is unique among rare earth ions in having an optical transition in the telecommunication C band (1540 nm), making it particularly appealing for quantum communication applications. In this work, we use nano-scale resonators coupled to erbium-167 ions in yttrium orthosilicate crystals (^{167}Er ^{3+}:Y_{2}SiO_{5}).

We demonstrate quantum storage in two types of resonators. In a nanobeam photonic crystal resonator milled directly in ^{167}Er ^{3+}:Y_{2}SiO_{5}, we show storage of weak coherent states using the atomic frequency comb protocol. The storage fidelity for single photon states is estimated to be at least 93.7% ± 2.4% using decoy state analysis, Storage of up to 10 μs and multimode storage are demonstrated. Using a hybrid amorphous silicon ^{167}Er ^{3+}:Y_{2}SiO_{5} resonator and on-chip electrodes, we demonstrate a multifunctional memory using the atomic frequency comb protocol with DC Stark shift control. In addition dynamic control of memory time, Stark shift control allows modifications to the frequency and bandwidth of stored light. We show tuning of the output pulse by ± 20 MHz relative to the input pulse, and broadening of the pulse bandwidth by more than a factor of three. The storage efficiency in both devices was limited to < 1%.

On the way to these results, we describe ^{167}Er ^{3+}:Y_{2}SiO_{5} spectroscopy measurements including optical coherence times and hyperfine lifetimes below 1 K, and we estimate the linear DC stark shift along two crystal directions. The design and fabrication of the on-chip resonators is presented. We discuss the limitations to storage time and efficiency, including superhyperfine coupling and resonator parameters, and we outline a path forward for improving the storage efficiency in these types of devices.

ID: CaltechTHESIS:06012020-134801698

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Abstract:

This thesis describes two studies of the dynamics of many-body quantum systems with extensive numerical support.

In Part I we first give a new algorithm for simulating the dynamics of one-dimensional systems that thermalize (that is, come to local thermal equilibrium). The core of this algorithm is a new truncation for matrix product operators, which reproduces local properties faithfully without reproducing non-local properties (e.g. the information required for OTOCs). To the extent that the dynamics depends only on local operators, timesteps interleaved with this truncation will reproduce that dynamics.

We then apply this to algorithm to Floquet systems: first to clean, non-integrable systems with a high-frequency drive, where we find that the system is well-described by a natural diffusive phenomenology; and then to disordered systems with low-frequency drive, which display diffusion — not subdiffusion — at appreciable disorder strengths.

In Part II, we study the utility of many-body localization as a medium for a thermodynamic engine. We first construct a small ("mesoscale") engine that gives work at high efficiency in the adiabatic limit, and show that thanks to the slow spread of information in many body localized systems, these mesoscale engines can be chained together without specially engineered insulation. Our construction takes advantage of precisely the fact that MBL systems do *not* thermalize. We then show that these engines still have high efficiency when run at finite speed, and we compare to competitor engines.

ID: CaltechTHESIS:05292019-112014488

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Abstract:

Mechanical resonators are used in a wide variety of technical applications, from precision time keeping and sensing, to the delay and filtering of microwave signals in mobile communication systems. Critical to many of these applications is the ability of a mechanical object to store vibrational energy at a well defined frequency of oscillation and with minimal damping. Energy damping can occur through acoustic radiation into the resonator support structure, or through impurities and defects in the resonator material, and is highly dependent on the temperature of operation due to the inherent anharmonic motion of atoms within solid-state materials. Here, we present optical measurements down to milliKelvin temperatures of the acoustic mode properties of a crystalline silicon nanobeam cavity incorporating a three-dimensional phononic bandgap support structure for acoustic confinement. Utilizing pulsed laser light to excite a co-localized optical mode of the optomechanical crystal (OMC) device, we are able to measure the dynamics of the internal cavity acoustic modes which are coupled to the light field via radiation pressure. These measurements represent an almost ideal scenario in which the ringdown occurs free of any additional mechanical or probe field contact, and where elastic scattering or radiation of the acoustic field does not lead to energy damping due to the full bandgap shield. The resulting ringdown measurements for the fundamental 5 GHz acoustic mode of the cavity show an exponential increase in phonon lifetime versus phononic shield period number, which at a bath temperature of 35 milliKelvin saturates above six periods to a value as long as 1.5 seconds. This ultra-long lifetime, corresponding to an effective phonon propagation length of several kilometers, is found at the lowest temperatures to be consistent with damping from non-resonant tunneling states whose energy lies below the acoustic shield phononic bandgap, and which are most likely present in the amorphous etch-damaged region of the silicon surface. Other, more rapid forms of damping such as resonant tunneling state damping or three-phonon scattering are suppressed due to the phononic bandgap shield and the reduced density of phonon states in the effectively one-dimensional nanobeam geometry. Prospects for newapplications of ultra-coherent nanoscale mechanical resonators include tests of various collapse models of quantum mechanics, or, if appropriately integrated with microwave superconducting quantum circuits, as miniature quantum memory or processing units with potentially many-orders of magnitude longer coherence time than their electromagnetic counterparts.

ID: CaltechTHESIS:03082019-114637094

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Abstract:

Quantum light-matter interfaces that can reversibly map quantum information between photons and atoms are essential for building future quantum networks. Crystals doped with rare-earth ions (REIs) are an attractive solid-state platform for such light-matter interfaces due to their exceptional optical and spin coherence properties at cryogenic temperatures. Building scalable REI-based technology has proven to be challenging due to the inherently weak coupling of REIs with light. This thesis explores the integration of REIs with nanophotonic resonators to overcome this weak light-matter interaction and enable efficient, scalable quantum light-matter interfaces. Specifically, this work focuses on the development of quantum nanophotonics with ytterbium in yttrium orthovanadate.

This thesis begins with an introduction to a nanophotonic platform based on photonic crystal cavities fabricated directly in rare-earth host materials and highlights the initial successes of this platform with neodymium-doped materials. This motivates an examination of the optical and spin coherence properties of ^{171}Yb:YVO_{4}, a REI material that was previously unexplored for quantum technology applications. This material is found to have strong optical transitions compared to other REI-doped materials, a simple energy level structure, and long optical and spin coherence lifetimes.

The focus then turns to the detection and coherent manipulation of single ytterbium ions coupled to nanophotonic cavities. The Purcell-enhancement in these cavities enables efficient optical detection and spin initialization of individual ytterbium ions. We identify ions corresponding to different isotopes of ytterbium and show that the coupling of electron and nuclear spin in ytterbium-171 at zero-field gives rise to strong electron-spin-like transitions that are first-order insensitive to magnetic field fluctuations. This allows for coherent microwave control and the observation of long spin coherence lifetimes at temperatures up to 1 K. We then make use of the optical selection rules and energy structure of ^{171}Yb:YVO_{4} to demonstrate high-fidelity single-shot optical readout of the spin state. These results establish nanophotonic devices in ^{171}Yb:YVO_{4} as a promising platform for solid-state quantum light-matter interfaces.

ID: CaltechTHESIS:03132019-062905529

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Abstract:

In this thesis, we study gapped topological phases of matter in systems with strong inter-particle interaction. They are challenging to analyze theoretically, because interaction not only gives rise to a plethora of phases that are otherwise absent, but also renders methods used to analyze non-interacting systems inadequate. By now, people have had a relatively systematic understanding of topological orders in two spatial dimensions. However, less is known about the higher dimensional cases. In Chapter 2, we will explore three dimensional long-range entangled topological orders in the framework of Walker-Wang models, which are a class of exactly solvable models for three-dimensional topological phases that are not known previously to be able to capture these phases. We find that they can represent a class of twisted discrete gauge theories, which were discovered using a different formalism. Meanwhile, a systematic theory of bosonic symmetry protected topological (SPT) phases in all spatial dimensions have been developed based on group cohomology. A generalization of the theory to group supercohomology has been proposed to classify and characterize fermionic SPT phases in all dimensions. However, it can only handle cases where the symmetry group of the system is a product of discrete unitary symmetries. Furthermore, the classification is known to be incomplete for certain symmetries. In Chapter 3, we will construct an exactly solvable model for the two-dimensional time-reversal-invariant topological superconductors, which could be valuable as a first attempt to a systematic understanding of strongly interacting fermionic SPT phases with anti-unitary symmetries in terms of exactly solvable models. In Chapter 4, we will propose an alternative classification of fermionic SPT phases using the spin cobordism theory, which hopefully can capture all the phases missing in the supercohomology classification. We test this proposal in the case of fermionic SPT phases with Z_{2} symmetry, where Z_{2} is either time-reversal or an internal symmetry. We find that cobordism classification correctly describes all known fermionic SPT phases in space dimensions less than or equal to 3.

ID: CaltechTHESIS:04242019-205929726

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Abstract:

Antiferromagnets are choice systems to study quantum critical behavior. Unlike ferromagnets, they can experience continuous quantum phase transitions when tuned by pressure. However, the lack of a net magnetization renders experimental approaches difficult and often indirect. Here I demonstrate that both non-resonant and resonant x-ray magnetic diffraction under pressure provide the highly-desired direct probe for microscopic insights into the disappearance of the magnetic order, as well as the evolution of the charge and structural degrees of freedom. In Mo_{3}Sb_{7}, where spins are itinerant with small magnetic moments, we have discovered the doubling of the superconducting transition temperature under pressure and relate it to a lattice change from tetragonal to cubic structure. In MnP, a spiral magnetic order with tightened pitch was revealed in the high-pressure phase near a superconducting state at ∼7 GPa. As the spiral pitch changes, fluctuations move from antiferromagnetic to ferromagnetic at long and short wavelengths, respectively, thereby potentially pro- moting spin-fluctuation-mediated superconductivity of different symmetries. In the all-in-all-out (AIAO) pyrochlore antiferromagnet Cd_{2}Os_{2}O_{7}, we discovered an anti- ferromagnetic quantum critical point at 35.8 GPa using new techniques for resonant x-ray magnetic diffraction under pressure. The continuous suppression of AIAO antiferromagnetic order to zero temperature is accompanied by inversion symmetry breaking of the lattice, dividing the *P − T* phase space into three regions of different time reversal and spatial inversion symmetries. While phase lines of opposite curvature indicate a striking departure from a mean-field form at high pressure, the intertwined spin, charge, and phonon fluctuation modes point to a strong-coupled scenario of quantum criticality.

ID: CaltechTHESIS:05102018-115838454

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Abstract:

Quantum chaos entails an entropic and computational obstruction to describing a system and thus is intrinsically difficult to characterize. An understanding of quantum chaos is fundamentally related to the mechanism of thermalization in many-body systems and the quantum nature of black holes. In this thesis we adopt the view that quantum information theory provides a powerful framework in which to elucidate chaos in strongly-interacting quantum systems.

We first push towards a more precise understanding of chaotic dynamics by relating different diagnostics of chaos, studying the time-evolution of random matrix Hamiltonians, and quantifying random matrix behavior in physical systems. We derive relations between out-of-time ordered correlation functions, spectral quantities, and frame potentials to relate the scrambling of quantum information, decay of correlators, and Haar-randomness. We give analytic expressions for these quantities in random matrix theory to explore universal aspects of late-time dynamics. Motivated by our random matrix results, we define *k*-invariance in order to capture the onset of random matrix behavior in physical systems.

We then refine our diagnostics in order to study chaotic systems with symmetry by considering Haar-randomness with respect to quotients of the unitary group, and in doing so we generalize our quantum information machinery. We further consider extended random matrix ensembles in the context of strongly-interacting quantum systems dual to black holes. Lastly, we study operator growth in classes of random quantum circuits.

ID: CaltechTHESIS:06012018-143029746

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Abstract:

The field of tensor networks, kicked off in 1992 by Steve White's invention of the spectacularly successful density matrix renormalization group (DMRG) algorithm, has exploded in popularity in recent years. Tensor networks are poised to play a role in helping us solve some of the greatest open physics problems of our time, such as understanding the nature of high-temperature superconductivity and illuminating a theory of quantum gravity. DMRG and extensions based on a class of variational states known as tensor network states have been indispensable tools in helping us understand both numerically and theoretically the properties of complicated classical and quantum many-body systems. However, practical challenges to these techniques still remain, and algorithmic developments are needed before tensor network algorithms can be applied to more physics problems. In this thesis we present a variety of recent advancements to tensor network algorithms.

First we describe a DMRG-like algorithm for noninteracting fermions. Noninteracting fermions, naturally being gapless and therefore having high levels of entanglement, are actually a challenging setting for standard DMRG algorithms, and we believe this new algorithm can help with tensor network calculations in that setting.

Next we explain a new algorithm called the variational uniform matrix product state (VUMPS) algorithm that is a DMRG-like algorithm that works directly in the thermodynamic limit, improving upon currently available MPS-based methods for studying infinite 1D and quasi-1D quantum many-body systems.

Finally, we describe a variety of improvements to algorithms for contracting 2D tensor networks, a common problem in tensor network algorithms, for example for studying 2D classical statistical mechanics problems and 2D quantum many-body problems with projected entangled pair states (PEPS). One is a new variant of the corner transfer matrix renormalization group (CTMRG) algorithm of Nishino and Okunishi that improves the numerical stability for contracting asymmetric two-dimensional tensor networks compared to the most commonly used method. Another is the application of the VUMPS algorithm to contracting 2D tensor networks. The last is a new alternative to CTMRG, where the tensors are solved for with eigenvalue equations instead of a power method, which we call the fixed point corner method (FPCM). We present results showing the transfer matrix VUMPS algorithm and FPCM significantly improve upon the convergence time of CTMRG. We expect these algorithms will play an important role in expanding the set of 2D classical and 2D quantum many-body problems that can be addressed with tensor networks.

ID: CaltechTHESIS:05312018-184631141

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Abstract: Chip-scale nonlinear optics can provide important new functions in communications, frequency metrology and spectroscopy. Optical microcavities enhance nonlinear optical effects through resonant recirculation. This recirculation dramatically reduces the required power in applications and also lowers signal noise. A key figure-of-merit is the optical Q factor, which provides a dimensionless scale of optical storage time within the microcavity. In this thesis, a novel integrated ultra-high-Q microcavity with Q as high as 230 million is presented. The device is applied to demonstrate multiple functions including electronic-rate soliton microcomb generation and stimulated Brillouin laser operation. For soliton generation, the resonator must be engineered to produce optical mode families that feature anomalous dispersion. This engineering is applied to generate solitons at wavelengths of 1064 nm and 778 nm. Systems-on-a-chip applications of these devices are discussed including compact optical synthesizers, optical clocks and rotation sensors. Finally, a compact array of silica ridge waveguides is described and applied for efficient and coherent ultraviolet-to-visible comb generation by dispersive-wave generation. Unlike other devices used to broaden spectra such as micro-structured fibers, these arrays provide a wide range of emission wavelength choices on a single chip. The arrays can also enable mode-locked lasers to attain greatly extended spectral reach for spectroscopy, bioimaging, tomography and metrology.

ID: CaltechTHESIS:11122017-215023206

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Abstract: Silicon technology provided a concrete basis of the integrated microelectronics revolution, and it might usher disruptive advances in photonics again. An integrated photonic system can potentially revolutionize instrumentation, time standards, spectroscopy, and navigation. Driven by these applications, various high-Q platforms have emerged over the last decade. However, applications require to satisfy challenging combinations of ultra-high-Q (UHQ) cavity performance, monolithic integration, and nonlinear cavity designs: the monolithic integration of UHQ devices still remains elusive. In this thesis, an integrated UHQ microcavity is demonstrated for the first time. A silicon nitride waveguide is monolithically integrated with a silicon oxide cavity, and the integrated waveguide can provide nearly universal interface to other photonic devices. Significantly, this thesis discusses far beyond setting a new record for integrated Q factor: the integrated UHQ cavity provides functionality as soliton source with electronic-repetition-rates. Demonstration of low-pump-power soliton generation at 15 GHz was previously possible in only discrete devices but essentially required for integrated self-referenced comb, which can unlock new level of performance and scale in an optoelectronic system. In addition, nonlinear cavity design is another outstanding challenge towards a further development on the optoelectronic system, and will be discussed in this thesis. The dispersion-engineered platform can potentially tailor the spectral bandwidth of frequency comb, and extend the frequency comb to visible and ultraviolet band. Importantly, the design methods are directly transferable to the integrated platform.

ID: CaltechThesis:10042017-102201104

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Abstract:

The results of this thesis concern the real-world realization of quantum computers, specifically how to build their "hard drives" or quantum memories. These are many-body quantum systems, and their building blocks are qubits, the same way bits are the building blocks of classical computers.

Quantum memories need to be robust against thermal noise, noise that would otherwise destroy the encoded information, similar to how strong magnetic field corrupts data classically stored in magnetic many-body systems (e.g., in hard drives). In this work I focus on a subset of many-body models, called quantum doubles, which, in addition to storing the information, could be used to perform the steps of the quantum computation, i.e., work as a "quantum processor".

In the first part of my thesis, I investigate how long a subset of quantum doubles (qudit surface codes) can retain the quantum information stored in them, referred to as their memory time. I prove an upper bound for this memory time, restricting the maximum possible performance of qudit surface codes.

Then, I analyze the structure of quantum doubles, and find two interesting properties. First, that the high-level description of doubles, utilizing only their quasi-particles to describe their states, disregards key components of their microscopic properties. In short, quasi-particles (anyons) of quantum doubles are not in a one-to-one correspondence with the energy eigenstates of their Hamiltonian. Second, by investigating phase transitions of a simple quantum double, D(S_{3}), I map its phase diagram, and interpret the physical processes the theory undergoes through terms borrowed from the Landau theory of phase transitions.

ID: CaltechTHESIS:05232018-150514177

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Abstract:

Combining quantum information theory (QIT) with thermodynamics unites 21st-century technology with 19th-century principles. The union elucidates the spread of information, the flow of time, and the leveraging of energy. This thesis contributes to the theory of quantum thermodynamics, particularly to QIT thermodynamics. The thesis also contains applications of the theory, wielded as a toolkit, across physics. Fields touched on include atomic, molecular, and optical physics; nonequilibrium statistical mechanics; condensed matter; high-energy physics; and chemistry. I propose the name *quantum steampunk* for this program. The term derives from the steampunk genre of literature, art, and cinema that juxtaposes futuristic technologies with 19th-century settings.

ID: CaltechTHESIS:05262018-061607919

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Abstract:

We describe a systematic way of producing fermionic topological phases using the technique of fermion condensation. We give a prescription for performing fermion condensation in bosonic topological phases which contain an emergent fermion. Our approach to fermion condensation can roughly be understood as coupling the parent bosonic topological phase to a phase of physical fermions, and condensing pairs of physical and emergent fermions. There are two distinct types of objects in fermionic theories, which we call “m-type” and “q-type” particles. The endomorphism algebras of q-type particles are complex Clifford algebras, and they have no analogues in bosonic theories. We construct a fermionic generalization of the tube category, which allows us to compute the quasiparticle excitations in fermionic topological phases. We then prove a series of results relating data in condensed theories to data in their parent theories; for example, if ** C** is a modular tensor category containing a fermion, then the tube category of the condensed theory satisfies

ID: CaltechTHESIS:05312018-132922155

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Abstract:

Understanding many-body quantum systems is one of the most challenging problems in contemporary condensed-matter physics. Tensor network representation of quantum states and operators are taking central stage in this pursuit and beyond. They prove to be a powerful numerical and conceptual tool, and indeed a new language altogether. This thesis investigates various aspects of these representations by focusing on two specific problems: the first half of the thesis is devoted to examining how 'stable' a tensor network representation is for two-dimensional quantum states with topological order, and the second half explores the representability of various unitary loop operators with tensor networks.

In the numerical usage of the tensor networks, the tensor is varied as to find the representation of the ground states of the given Hamiltonian. In chapter two and three of this thesis we show that such a numerical program for topological phases can be 'ill-posed'. We show that tensor network can be an unstable representation for a topological phase: even an infinitesimal variation in the representation results in the loss of topological order, completely or partially. We diagnose this problem by identifying the exact causes of this instability, and find that it is only tensor variations in certain directions that result in instability, because they result in the condensation of bosonic quasi-particles of the phase. Such unstable variations are characterized by two properties: (1) they can replace a tensor in the tensor network without making the network collapse, and (2) their presence in the network represents the presence of a non-trivial topological charge. We prove that the general tensor representation of all string-net models suffer with such instabilities. We propose an exact mathematical operator to project out all such unstable variations and show its efficacy for a few models by direct calculations. Such an operator can be useful in numerical programs involving such tensor representations. We also point out that such variations play a crucial role in simulating topological phase transitions and their presence can be vital in an accurate simulation.

In chapter four and five of this thesis we focus on the representability of unitary loop operators by tensor networks. Such operators not only provide an important tool in the study of dynamical process in one-dimensional systems, but also in understanding and classification of symmetry protected topological phases in two dimensions. To characterize all such operators, we find a necessary and sufficient condition for any loop tensor network operator of a given length to represent a unitary operator. In particular, it is shown that all unitary operators that map local operators to local operators (locality-preserving) can always be represented by a tensor network. Locality-preserving unitary loop operators are classified by a rational index called the GNVW index defined in Ref. [1] which measures how much information 'flows' along the loop. We define Rank-Ratio index for tensor network operators and show that it is completely equivalent to the GNVW index. Therefore, GNVW index of a unitary operator can be easily extracted from its tensor network representation. We find that, other than representing locality-preserving unitary maps, tensor networks can also represent unitary operators that map local operators to global (non-local) operators. These tensor network operators are found to have a long-ranged order similar to tensors that represent topological tensor network states in two dimensions.

ID: CaltechTHESIS:09122017-161101236

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Abstract:

This thesis is devoted to studying a class of quantum error-correcting codes — topological quantum codes. We explore the question of how one can achieve fault- tolerant quantum computation with topological codes. We treat quantum error-correcting codes not only as a compelling ingredient needed to build a quantum computer, but also as a useful theoretical tool in other areas of physics. In particular, we explore what insights topological codes can provide into challenging questions, such as the classification of quantum phases of matter.

In this thesis, we focus on a family of topological codes — color codes, which are particularly intriguing due to the rich physics they display and their computational power. We start by introducing color codes and explaining their basic properties. Then, we show how to perform fault-tolerant universal quantum computation with three-dimensional color codes by transverse gates and code switching. We later compare the resource overhead of the code-switching approach with that of a state distillation scheme. We discuss how to perform error correction with the toric and color codes, as well as introduce local decoders for those two families of codes. By exploiting a connection between error correction and statistical mechanics we estimate the storage threshold error rates for bit-flip and phase-flip noise in the three-dimensional color code. We finish by showing that the color and toric code families in d dimensions are equivalent in a sense of local unitary transformations and explore implications of this equivalence.

ID: CaltechTHESIS:05282018-173928314

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Abstract: This thesis introduces a new phase transitions in three dimensional quantum gravity. The main technical tools comes from the spectral theory of hyperbolic manifolds.

ID: CaltechTHESIS:06022018-013547962

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Abstract: In this work, we develop theoretical formulations to analyze experimentally relevant quantum measurement schemes in a general relativistic framework, and discuss their implications versus the Newtonian or non-relativistic viewpoints. Specifically, we address (i) matter waves in simple free fall, (ii) the Mach-Zehdner atom interferometer with light-matter interaction and (iii) optomechanical systems. The motivation is to explore the regime of physics where gravity and relativistic effects become pertinent for quantum experiments due to the increase in system size and complexity. Such experiments may illuminate a way forward to reconcile the independently successful but apparently paradoxical theories of gravity and quantum mechanics, where sound theoretical foundations are necessary to help guide the search for new physics at their interface.

ID: CaltechTHESIS:06082018-212416022

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Abstract:

Periodically-driven (Floquet) quantum systems are ubiquitous in science and technology. For example, when a laser illuminates a material or an AC voltage is applied to a device, the system is well-described by a time-periodic Hamiltonian. In recent years, periodic driving has been proposed, not just as a tool to excite and probe devices, but actually as a mechanism of *engineering* new phases of matter, some of which have no equilibrium analog. However, with this promise comes a serious problem. Intuitively, if energy is injected into and distributed throughout a system, it is no surprise that it tends to heat up indefinitely to infinite temperature.

In this thesis, we study the mechanisms of heating, i.e. the process of thermalization, in Floquet systems and propose methods to control them. Specifically, for non-interacting Floquet systems that are coupled to external bosonic and fermionic baths (e.g. laser-driven electrons in a semiconductor that interact with phonons and an external lead), we classify the relevant scattering processes that contribute to cooling/heating in the Floquet bands and suggest methods to suppress heating via bandwidth-restrictions on the baths. We find that is possible, with appropriate dissipative engineering, to stabilize a controlled incompressible nonequilibrium steady-state resembling a ground state - a state we term the "Floquet insulator." We extend this analysis to include short-range interactions that contribute additional heating processes and show, under the same framework, that heating can be controlled with dissipation. In the process, we develop a simple effective model for the Floquet band densities that captures the essence of all the Floquet scattering processes and that is useful for ballparking experimentally-relevant estimates of heating. Next, we turn our attention to strongly-interacting closed Floquet systems and study how heating emerges through a proliferation of resonances. We find a novel integrable point governing the strong-interaction limit of the Floquet system and examine the breakdown of integrability via the proliferation of resonances. We observe two distinct scaling regimes, attributed to non-thermal and thermal behavior, and discover a power-law scaling of the crossover between them as a function of system size. The lingering ergodicity-breaking effects of the conserved quantities in the vicinity (in parameter space) of the integrable point at finite size is a phenomena we term "near-integrability." These results suggest that small quantum systems, which are accessible currently in many platforms (e.g. trapped ions, cold atoms, superconducting devices), intrinsically host non-thermal states that one may be able to utilize to avoid heating. Furthermore, our results suggest a "dual" interpretation, in the thermodynamic limit, that a periodically-driven system exhibits prethermalization as a power-law in interaction strength.

ID: CaltechTHESIS:06062018-171256773

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Abstract: New opportunities for optical physics emerge from the integration of cold atoms with nanophotonic devices. Due to their small optical loss and tight field confinement, these nanoscale dielectric devices are capable of mediating strong atom-light interactions and open new avenues for quantum transport and quantum many-body phenomena. In particular, coupling atoms to the band edge of a photonic crystal waveguide (PCW) provides a unique platform for generating tunable range coherent atom-atom interactions which are mediated by the guided mode photons.

ID: CaltechTHESIS:06082017-062231802

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Abstract: Generating nonclassical states of a macroscopic mechanical object has been a subject of considerable interest. It offers a route toward fundamental test of quantum mechanics in an unexplored regime. However, a macroscopic quantum state is very susceptible to decoherence due to the environment. One way to generate robust quantum states is quantum reservoir engineering. In this work, we utilize the reservoir engineering scheme to generate a steady quantum squeezed state of a micron-scale mechanical oscillator in an electromechanical system. Together with the backaction evading measurement technique, we demonstrate a quantum nondemolition measurement of the mechanical quadratures to characterize the quantum squeezed state. By measuring the quadrature variances of the mechanical motion, more than 3dB squeezing below the zero-point level has been achieved.

ID: CaltechTHESIS:10182016-152744850

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Abstract:

Development of technology can allow access to new regimes in science and creation of new fields of research. The development of ultra-high finesse mirror technology enabled the development of the field of cavity quantum electrodynamics, and an abundance of wonderful physics experiments soon followed. The sophistication of the field of nano-fabrication and nano-photonics would allow unprecedented capability to mold the shape and flow of light, and provide a novel platform for efficient and hopefully integrable quantum systems. In this project, we hope to interface cold atoms, perhaps the most quintessential of quantum systems, to the engineering power of nano-photonics. We believe this field of study will not only lead to the demonstration of new physics in the quantum regime, but work toward building a network with quantum capabilities mediated by optical channels.

In this project, we develop a nano-fabricated platform capable of interfacing nano-photonic devices with cold Cesium atoms in free-space. Nano-photonic waveguide devices are fabricated in a Silicon Nitride device layer on Silicon substrate. The fabrication is compatible with conventional semiconductor fabrication processes, and the chip design has been adapted to allow incorporation with free-space optics to support cold Cesium atom cloud around the waveguides. An ultra-high vacuum system that is compatible to the chip and its supporting structures was constructed to perform experiments.

With our system, we were able to fabricate and characterize nano-photonic structures, including 1D photonic crystal waveguides, cavities, and 2D photonic crystal slabs. For the 1D photonic crystal waveguide devices, enhanced atom-light coupling between localized Cesium atoms in the vicinity of the devices, and also atom-atom interaction between Cesium atoms mediated by the guided mode of the photonic crystal waveguide, has been observed. The 2D photonic devices allow us many capabilities beyond that of the 1D waveguide. Demonstration of exotic optical properties including natural decay rate suppression and circular polarization engineering, should be within reach in the near future.

ID: CaltechTHESIS:06022017-134307910

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Abstract:

The growing interest in optical quantum systems has led to the exploration of multiple platforms. Though pioneering experiments were performed in trapped atom and trapped ion systems, solid state systems show promise of being scalable and robust. Rare earth dopants in crystalline hosts are an appealing option because they possess a rich spectrum of energy levels that result from a partially filled electron orbital. While level structure varies across the period, all elements possess crystal field splittings corresponding to near infra-red or optical frequencies, as well as Zeeman and often hyperfine levels separated by radio frequency and microwave frequencies. These levels demonstrate long excited-state lifetimes and coherence times and have been used in diverse applications, including demonstrating storage of a photonic state, converting of optical to microwave photons, and manipulating a single ion as a single qubit. The ions' weak interaction with their environment results in low coupling to optical fields, which had previously required measurements with macroscopically large ensembles of ions. Coupling the ions to an optical cavity enables the use of a smaller ensemble, which is required for the development of the aforementioned technologies in an on-chip scalable architecture.

This thesis contains recent progress towards fabricating optical micro and nanocavities coupled to ensembles of erbium ions, mainly erbium in yttrium orthosilicate. In one design, focused ion beam milling was used to create a triangular nanobeam photonic crystal cavity in a bulk erbium-doped substrate. A second design leveraged the fabrication capabilities of silicon photonics, defining amorphous silicon ring resonators using electron beam lithography and dry etching. These devices coupled evanescently to erbium ions below the ring, in the bulk substrate. Simulation, design, fabrication, and characterization of both resonators are discussed. Coupling between the ions and the resonator is demonstrated for each, and capabilities offered by these devices are described. Preliminary work implementing coherent control of erbium ions is presented. Lastly, alternative substrates are evaluated for possible future solid-state erbium systems.

ID: CaltechTHESIS:03152017-114949088

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Abstract:

Integrating ultracold atoms with nanophotonics enables the exploration of new paradigms in quantum optics and many body physics. Advanced fabrication capabilities for low-loss dielectric materials provide powerful tools to engineer light-matter coupling of photons and atoms. For example, dispersion-engineered photonic crystal waveguides (PCWs) permit not only stable trapping and probing of atoms via interactions with guided mode (GM) light, but also the possibility to study the physics of strong photon-mediated interactions between atoms. This thesis describes the design of a quasi-one-dimensional structure, the alligator photonic crystal waveguide (APCW), which has already allowed for the observation of some of those features.

Furthermore, external illumination schemes allow for the trapping and transport of atoms near the dielectric device. Here, atoms loaded into a one-dimensional optical lattice are transported through the APCW. As the atoms trapped in the lattice approach the APCW, the combination of lattice and GM potential can smoothly guide atoms into the gap between the two dielectric nanobeams. Therefore, the transmission of a weak guided mode probe is modulated at the rate determined by the lattice moving through the APCW. In the near future, single atoms can then be transferred from the moving lattice into optical traps formed in each unit cell by GMs of the APCW. Moreover, a characterization of a simple 2D photonic crystal slabs design is presented.

ID: CaltechTHESIS:05152017-144541997

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Abstract:

Optical micro-resonators have been studied for decades as a platform to investigate optical physics, and to miniaturize bulky optical systems. In the last decade, optical frequency combs, which have revolutionized the precision measurement of time and frequency, have been demonstrated in optical micro-resonators via the combined effect of parametric oscillation and cascaded four-wave mixing. More recently, soliton mode-locking has made possible low-noise/reproducible generation of these miniature combs (microcombs). In this thesis, we demonstrated the generation of soliton microcombs from silica wedge disk micro-resonators and the characteristics of the soliton microcombs are described. We also applied soliton microcombs to dual-comb spectroscopy and distance measurement (LIDAR) for the first time. Also, ways to improve spectral resolution, signal-to-noise ratio, and spectral coverage are discussed. In addition to soliton microcombs, a novel spiral resonator is studied as a stable optical frequency reference. Combined with a frequency comb, this new type of chip-based reference cavity is also applied to generate stable microwaves via optical frequency division. Lastly, we generated a stimulated Brillouin laser (SBL) from the optical micro-resonator and its phonon-limited linewidth is studied. Application of the SBL for rotation measurement is also demonstrated. This thesis is organized into six chapters. Throughout the thesis, the implication and potential of my PhD work toward chip-based advanced optics system are discussed.

ID: CaltechTHESIS:06012017-163114372

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Abstract:

This thesis comprises studies of 3*d*-5*d* transition metal oxides with various degrees of electronic correlation using nonlinear harmonic generation rotational anisotropy as well as time-resolved optical reflectivity methods. Specifically, we explored photo-induced phase transition in Ca_{2}RuO_{4} and Sr_{2}IrO_{4}, discovered novel electronic phases in doped Sr_{2}IrO_{4} and Sr_{3}Ir_{2}O_{7}, and investigated different types of antiferromagnetic orders in transition metal trichalcogenides MPX_{3}.

ID: CaltechTHESIS:06092017-141136995

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Abstract:

Strongly interacting systems of atoms and photons are an important resource in many active areas of research, including quantum information science, quantum simulation, and metrology. Frequently, the strength of these interactions is enhanced by using an optical resonator to confine light to a small volume. In recent years, there have been efforts to replace traditional Fabry–Pérot resonators, formed from macroscopic mirrors, with micro- and nano-fabricated systems, leveraging techniques and infrastructure from semiconductor manufacture to scalably produce high-quality, small mode volume waveguides and resonators. Of particular interest are nano-fabricated photonic crystals, in which very fine control over modal and dispersion properties is possible. Here I describe our efforts to reliably produce photonic crystal waveguides with guided modes designed to trap and interrogate an array of ultracold cesium atoms. Specifically, I present models capturing band placement, modal structure, finite photonic crystal effects, and waveguide input and output coupling; I discuss the techniques we use to fabricate our photonic crystal waveguides; and I describe our characterization capabilities and the packaging and installation of the waveguides into the atomic physics system.

ID: CaltechTHESIS:06082017-134311664

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Abstract:

We investigate a many-body localized 1d spin chain with a Hamiltonian consisting of classical disordered Ising and a small transversal field. An existing perturbative diagonalization by Imbrie is simplified and reinterpreted in order to prove the anticipated form of the Lieb-Robinson bound and the area law in an eigenstate. We also show how to approximately reduce Imbrie’s unitary to a finite depth circuit. The concept of resonances in Imbrie’s work can be given a physical meaning as an avoided crossing of levels as functions of a magnetic field. For a slow drive of this field, we discuss the proofs of validity for an efficient classical simulation of such disordered systems, both isolated and in contact with the environment. Our results are applicable to Floquet systems and describe an unexpected mechanism of heating up over long times. We also revisit noisy quantum adiabatic annealers like the D-wave machine and find a nontrivial physics that can possibly be observed in them.

ID: CaltechTHESIS:06052017-155729766

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Abstract:

The bilayer quantum Hall state at total filling factor *ν _{T}=1*, where the total electron density matches the degeneracy of the lowest Landau level, is a prominent example of Bose-Einstein condensation of excitons. A macroscopically ordered state is realized where an electron in one layer is tightly bound to a "hole" in the other layer. If exciton transport were the only bulk transportmechanism, a current driven in one layer would spontaneously generate a current of equal magnitude and opposite sign in the other layer. The Corbino Coulomb drag measurements presented in this thesis demonstrate precisely this phenomenon.

Excitonic superfluidity has been long sought in the *ν _{T}=1* state. The tunneling between the two electron gas layers exihibit a

ID: CaltechTHESIS:09232015-145320310

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Abstract:

Thermodynamical fluctuations in temperature and position exist in every physical system, and show up as a fundamental noise limit whenever we choose to measure some quantity in a laboratory environment. Thermodynamical fluctuations in the position of the atoms in the dielectric coatings on the mirrors for optical cavities at the forefront of precision metrology (e.g., LIGO, the cavities which probe atomic transitions to define the second) are a current limiting noise source for these experiments, and anything which involves locking a laser to an optical cavity. These thermodynamic noise sources scale physical geometry of experiment, material properties (such as mechanical loss in our dielectric coatings), and temperature. The temperature scaling provides a natural motivation to move to lower temperatures, with a potential huge benefit for redesigning a room temperature experiment which is limited by thermal noise for cryogenic operation.

We design, build, and characterize a pair of linear Fabry-Perot cavities to explore limitations to ultra low noise laser stabilization experiments at cryogenic temperatures. We use silicon as the primary material for the cavity and mirrors, due to a zero crossing in its linear coefficient of thermal expansion (CTE) at 123 K, and other desirable material properties. We use silica tantala coatings, which are currently the best for making high finesse low noise cavities at room temperature. The material properties of these coating materials (which set the thermal noise levels) are relatively unknown at cryogenic temperatures, which motivates us to study them at these temperatures. We were not able to measure any thermal noise source with our experiment due to excess noise. In this work we analyze the design and performance of the cavities, and recommend a design shift from mid length cavities to short cavities in order to facilitate a direct measurement of cryogenic coating noise.

In addition, we measure the cavities (frequency dependent) photo-thermal response. This can help characterize thermooptic noise in the coatings, which is poorly understood at cryogenic temperatures. We also explore the feasibility of using the cavity to do macroscopic quantum optomechanics such as ground state cooling.

ID: CaltechTHESIS:01042016-150434876

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Abstract:

This thesis presents studies of the role of disorder in non-equilibrium quantum systems. The quantum states relevant to dynamics in these systems are very different from the ground state of the Hamiltonian. Two distinct systems are studied, (i) periodically driven Hamiltonians in two dimensions, and (ii) electrons in a one-dimensional lattice with power-law decaying hopping amplitudes. In the first system, the novel phases that are induced from the interplay of periodic driving, topology and disorder are studied. In the second system, the Anderson transition in *all* the eigenstates of the Hamiltonian are studied, as a function of the power-law exponent of the hopping amplitude.

In periodically driven systems the study focuses on the effect of disorder in the nature of the topology of the steady states. First, we investigate the robustness to disorder of Floquet topological insulators (FTIs) occurring in semiconductor quantum wells. Such FTIs are generated by resonantly driving a transition between the valence and conduction band. We show that when disorder is added, the topological nature of such FTIs persists as long as there is a gap at the resonant quasienergy. For strong enough disorder, this gap closes and all the states become localized as the system undergoes a transition to a trivial insulator.

Interestingly, the effects of disorder are not necessarily adverse, disorder can also induce a transition from a trivial to a topological system, thereby establishing a Floquet Topological Anderson Insulator (FTAI). Such a state would be a dynamical realization of the topological Anderson insulator. We identify the conditions on the driving field necessary for observing such a transition. We realize such a disorder induced topological Floquet spectrum in the driven honeycomb lattice and quantum well models.

Finally, we show that two-dimensional periodically driven quantum systems with spatial disorder admit a unique topological phase, which we call the anomalous Floquet-Anderson insulator (AFAI). The AFAI is characterized by a quasienergy spectrum featuring chiral edge modes coexisting with a fully localized bulk. Such a spectrum is impossible for a time-independent, local Hamiltonian. These unique characteristics of the AFAI give rise to a new topologically protected nonequilibrium transport phenomenon: quantized, yet nonadiabatic, charge pumping. We identify the topological invariants that distinguish the AFAI from a trivial, fully localized phase, and show that the two phases are separated by a phase transition.

The thesis also present the study of disordered systems using Wegner's Flow equations. The Flow Equation Method was proposed as a technique for studying excited states in an interacting system in one dimension. We apply this method to a one-dimensional tight binding problem with power-law decaying hoppings. This model presents a transition as a function of the exponent of the decay. It is shown that the the entire phase diagram, i.e. the delocalized, critical and localized phases in these systems can be studied using this technique. Based on this technique, we develop a strong-bond renormalization group that procedure where we solve the Flow Equations iteratively. This renormalization group approach provides a new framework to study the transition in this system.

ID: CaltechTHESIS:05262016-092645359

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Abstract:

The optomechanical interaction is an extremely powerful tool with which to measure mechanical motion. The displacement resolution of chip-scale optomechanical systems has been measured on the order of 1⁄10th of a proton radius. So strong is this optomechanical interaction that it has recently been used to remove almost all thermal noise from a mechanical resonator and observe its quantum ground-state of motion starting from cryogenic temperatures.

In this work, chapter 1 describes the basic physics of the canonical optomechanical system, optical measurement techniques, and how the optomechanical interaction affects the coupled mechanical resonator. In chapter 2, we describe our techniques for realizing this canonical optomechanical system in a chip-scale form factor.

In chapter 3, we describe an experiment where we used radiation pressure feedback to cool a mesoscopic mechanical resonator near its quantum ground-state from room-temperature. We cooled the resonator from a room temperature phonon occupation of <n> = 6.5 million to an occupation of <n> = 66, which means the resonator is in its ground state approximately 2% of the time, while being coupled to a room-temperature thermal environment. At the time of this work, this is the closest a mesoscopic mechanical resonator has been to its ground-state of motion at room temperature, and this work begins to open the door to room-temperature quantum control of mechanical objects.

Chapter 4 begins with the realization that the displacement resolutions achieved by optomechanical systems can surpass those of conventional MEMS sensors by an order of magnitude or more. This provides the motivation to develop and calibrate an optomechanical accelerometer with a resolution of approximately 10 micro-g/rt-Hz over a bandwidth of approximately 30 kHz. In chapter 5, we improve upon the performance and practicality of this sensor by greatly increasing the test mass size, investigating and reducing low-frequency noise, and incorporating more robust optical coupling techniques and capacitive wavelength tuning. Finally, in chapter 6 we present our progress towards developing another optomechanical inertial sensor - a gyroscope.

ID: CaltechTHESIS:01122016-170853872

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Abstract: We demonstrate the utility of superfluid helium-4 as an extremely low loss optomechanical element. We form an optomechanical system with a cylindrical niobium superconducting TE_{011} resonator whose 40 cm^{3} inner cylindrical cavity is filled with ^{4}He. [1] Coupling is realized via the variations in permittivity resulting from the density profile of the acoustic modes. Acoustic losses in helium-4 below 500 mK are governed by the intrinsic nonlinearity of sound, leading to an attenuation which drops as *T* ^{4}, indicating the possibility of quality factors (Q) over 10^{10} at 10 mK. In our lowest loss mode, we demonstrate this *T* ^{4} law down to 50 mK, realizing an acoustic Q of 1.35·10^{8} at 8.1 kHz. When coupled with a low phase noise microwave source, we expect this system to be utilized as a probe of macroscopic quantized motion, for precision measurements to search for fundamental physical length scales, and as a continuous gravitational wave detector. Our estimates suggest that a resonant superfluid acoustic system could exceed the sensitivity of current broad-band detectors for narrow-band sources such as pulsars [2].

ID: CaltechTHESIS:05272016-075803376

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Abstract:

In the field of mechanics, it is a long standing goal to measure quantum behavior in ever larger and more massive objects. It may now seem like an obvious conclusion, but until recently it was not clear whether a macroscopic mechanical resonator -- built up from nearly 10^{13} atoms -- could be fully described as an ideal quantum harmonic oscillator. With recent advances in the fields of opto- and electro-mechanics, such systems offer a unique advantage in probing the quantum noise properties of macroscopic electrical and mechanical devices, properties that ultimately stem from Heisenberg's uncertainty relations. Given the rapid progress in device capabilities, landmark results of quantum optics are now being extended into the regime of macroscopic mechanics.

The purpose of this dissertation is to describe three experiments -- motional sideband asymmetry, back-action evasion (BAE) detection, and mechanical squeezing -- that are directly related to the topic of measuring quantum noise with mechanical detection. These measurements all share three pertinent features: they explore quantum noise properties in a macroscopic electromechanical device driven by a minimum of two microwave drive tones, hence the title of this work: "Quantum electromechanics with two tone drive".

In the following, we will first introduce a quantum input-output framework that we use to model the electromechanical interaction and capture subtleties related to interpreting different microwave noise detection techniques. Next, we will discuss the fabrication and measurement details that we use to cool and probe these devices with coherent and incoherent microwave drive signals. Having developed our tools for signal modeling and detection, we explore the three-wave mixing interaction between the microwave and mechanical modes, whereby mechanical motion generates motional sidebands corresponding to up-down frequency conversions of microwave photons. Because of quantum vacuum noise, the rates of these processes are expected to be unequal. We will discuss the measurement and interpretation of this asymmetric motional noise in a electromechanical device cooled near the ground state of motion.

Next, we consider an overlapped two tone pump configuration that produces a time-modulated electromechanical interaction. By careful control of this drive field, we report a quantum non-demolition (QND) measurement of a single motional quadrature. Incorporating a second pair of drive tones, we directly measure the measurement back-action associated with both classical and quantum noise of the microwave cavity. Lastly, we slightly modify our drive scheme to generate quantum squeezing in a macroscopic mechanical resonator. Here, we will focus on data analysis techniques that we use to estimate the quadrature occupations. We incorporate Bayesian spectrum fitting and parameter estimation that serve as powerful tools for incorporating many known sources of measurement and fit error that are unavoidable in such work.

ID: CaltechTHESIS:01072016-143812513

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Abstract:

The subject of this thesis is the measurement and interpretation of thermopower in high-mobility two-dimensional electron systems (2DESs). These 2DESs are realized within state-of-the-art GaAs/AlGaAs heterostructures that are cooled to temperatures as low as T = 20 mK. Much of this work takes place within strong magnetic fields where the single-particle density of states quantizes into discrete Landau levels (LLs), a regime best known for the quantum Hall effect (QHE). In addition, we review a novel hot-electron technique for measuring thermopower of 2DESs that dramatically reduces the influence of phonon drag.

Early chapters concentrate on experimental materials and methods. A brief overview of GaAs/AlGaAs heterostructures and device fabrication is followed by details of our cryogenic setup. Next, we provide a primer on thermopower that focuses on 2DESs at low temperatures. We then review our experimental devices, temperature calibration methods, as well as measurement circuits and protocols.

Latter chapters focus on the physics and thermopower results in the QHE regime. After reviewing the basic phenomena associated with the QHE, we discuss thermopower in this regime. Emphasis is given to the relationship between diffusion thermopower and entropy. Experimental results demonstrate this relationship persists well into the fractional quantum Hall (FQH) regime.

Several experimental results are reviewed. Unprecedented observations of the diffusion thermopower of a high-mobility 2DES at temperatures as high as T = 2 K are achieved using our hot-electron technique. The composite fermion (CF) effective mass is extracted from measurements of thermopower at LL filling factor ν = 3/2. The thermopower versus magnetic field in the FQH regime is shown to be qualitatively consistent with a simple entropic model of CFs. The thermopower at ν = 5/2 is shown to be quantitatively consistent with the presence of non-Abelian anyons. An abrupt collapse of thermopower is observed at the onset of the reentrant integer quantum Hall effect (RIQHE). And the thermopower at temperatures just above the RIQHE transition suggests the existence of an unconventional conducting phase.

ID: CaltechTHESIS:12122015-165527858

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Abstract: The work in this thesis splits naturally into two parts: (1) experimentally oriented work consisting of experimental proposals for systems that could be used to implement quantum information tasks with current technology, and (2) theoretical work focusing on universal fault-tolerant quantum computers which we hope can be scaled as experimental capabilities continue to move forward.

ID: CaltechTHESIS:06072016-162802972

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Abstract: An exciting frontier in quantum information science is the integration of otherwise "simple" quantum elements into complex quantum networks. The laboratory realization of even small quantum networks enables the exploration of physical systems that have not heretofore existed in the natural world. Within this context, there is active research to achieve nanoscale quantum optical circuits, for which atoms are trapped near nano-scopic dielectric structures and "wired" together by photons propagating through the circuit elements. Single atoms and atomic ensembles endow quantum functionality for otherwise linear optical circuits and thereby enable the capability of building quantum networks component by component. Toward these goals, we have experimentally investigated three different systems, from conventional to rather exotic systems : free-space atomic ensembles, optical nano fibers, and photonics crystal waveguides. First, we demonstrate measurement-induced quadripartite entanglement among four quantum memories. Next, following the landmark realization of a nanofiber trap, we demonstrate the implementation of a state-insensitive, compensated nanofiber trap. Finally, we reach more exotic systems based on photonics crystal devices. Beyond conventional topologies of resonators and waveguides, new opportunities emerge from the powerful capabilities of dispersion and modal engineering in photonic crystal waveguides. We have implemented an integrated optical circuit with a photonics crystal waveguide capable of both trapping and interfacing atoms with guided photons, and have observed the collective effect, superradiance, mediated by the guided photons. These advances provide an important capability for engineered light-matter interactions, enabling explorations of novel quantum transport and quantum many-body phenomena.

ID: CaltechTHESIS:05202015-155217795

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Abstract:

With the advent of the laser in the year 1960, the field of optics experienced a renaissance from what was considered to be a dull, solved subject to an active area of development, with applications and discoveries which are yet to be exhausted 55 years later. Light is now nearly ubiquitous not only in cutting-edge research in physics, chemistry, and biology, but also in modern technology and infrastructure. One quality of light, that of the imparted radiation pressure force upon reflection from an object, has attracted intense interest from researchers seeking to precisely monitor and control the motional degrees of freedom of an object using light. These optomechanical interactions have inspired myriad proposals, ranging from quantum memories and transducers in quantum information networks to precision metrology of classical forces. Alongside advances in micro- and nano-fabrication, the burgeoning field of optomechanics has yielded a class of highly engineered systems designed to produce strong interactions between light and motion.

Optomechanical crystals are one such system in which the patterning of periodic holes in thin dielectric films traps both light and sound waves to a micro-scale volume. These devices feature strong radiation pressure coupling between high-quality optical cavity modes and internal nanomechanical resonances. Whether for applications in the quantum or classical domain, the utility of optomechanical crystals hinges on the degree to which light radiating from the device, having interacted with mechanical motion, can be collected and detected in an experimental apparatus consisting of conventional optical components such as lenses and optical fibers. While several efficient methods of optical coupling exist to meet this task, most are unsuitable for the cryogenic or vacuum integration required for many applications. The first portion of this dissertation will detail the development of robust and efficient methods of optically coupling optomechanical resonators to optical fibers, with an emphasis on fabrication processes and optical characterization.

I will then proceed to describe a few experiments enabled by the fiber couplers. The first studies the performance of an optomechanical resonator as a precise sensor for continuous position measurement. The sensitivity of the measurement, limited by the detection efficiency of intracavity photons, is compared to the standard quantum limit imposed by the quantum properties of the laser probe light. The added noise of the measurement is seen to fall within a factor of 3 of the standard quantum limit, representing an order of magnitude improvement over previous experiments utilizing optomechanical crystals, and matching the performance of similar measurements in the microwave domain.

The next experiment uses single photon counting to detect individual phonon emission and absorption events within the nanomechanical oscillator. The scattering of laser light from mechanical motion produces correlated photon-phonon pairs, and detection of the emitted photon corresponds to an effective phonon counting scheme. In the process of scattering, the coherence properties of the mechanical oscillation are mapped onto the reflected light. Intensity interferometry of the reflected light then allows measurement of the temporal coherence of the acoustic field. These correlations are measured for a range of experimental conditions, including the optomechanical amplification of the mechanics to a self-oscillation regime, and comparisons are drawn to a laser system for phonons. Finally, prospects for using phonon counting and intensity interferometry to produce non-classical mechanical states are detailed following recent proposals in literature.

ID: CaltechTHESIS:03312015-144223105

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Abstract:

Light has long been used for the precise measurement of moving bodies, but the burgeoning field of optomechanics is concerned with the interaction of light and matter in a regime where the typically weak radiation pressure force of light is able to push back on the moving object. This field began with the realization in the late 1960's that the momentum imparted by a recoiling photon on a mirror would place fundamental limits on the smallest measurable displacement of that mirror. This coupling between the frequency of light and the motion of a mechanical object does much more than simply add noise, however. It has been used to cool objects to their quantum ground state, demonstrate electromagnetically-induced-transparency, and modify the damping and spring constant of the resonator. Amazingly, these radiation pressure effects have now been demonstrated in systems ranging 18 orders of magnitude in mass (kg to fg).

In this work we will focus on three diverse experiments in three different optomechanical devices which span the fields of inertial sensors, closed-loop feedback, and nonlinear dynamics. The mechanical elements presented cover 6 orders of magnitude in mass (ng to fg), but they all employ nano-scale photonic crystals to trap light and resonantly enhance the light-matter interaction. In the first experiment we take advantage of the sub-femtometer displacement resolution of our photonic crystals to demonstrate a sensitive chip-scale optical accelerometer with a kHz-frequency mechanical resonator. This sensor has a noise density of approximately 10 micro-g/rt-Hz over a useable bandwidth of approximately 20 kHz and we demonstrate at least 50 dB of linear dynamic sensor range. We also discuss methods to further improve performance of this device by a factor of 10.

In the second experiment, we used a closed-loop measurement and feedback system to damp and cool a room-temperature MHz-frequency mechanical oscillator from a phonon occupation of 6.5 million down to just 66. At the time of the experiment, this represented a world-record result for the laser cooling of a macroscopic mechanical element without the aid of cryogenic pre-cooling. Furthermore, this closed-loop damping yields a high-resolution force sensor with a practical bandwidth of 200 kHZ and the method has applications to other optomechanical sensors.

The final experiment contains results from a GHz-frequency mechanical resonator in a regime where the nonlinearity of the radiation-pressure interaction dominates the system dynamics. In this device we show self-oscillations of the mechanical element that are driven by multi-photon-phonon scattering. Control of the system allows us to initialize the mechanical oscillator into a stable high-amplitude attractor which would otherwise be inaccessible. To provide context, we begin this work by first presenting an intuitive overview of optomechanical systems and then providing an extended discussion of the principles underlying the design and fabrication of our optomechanical devices.

ID: CaltechTHESIS:01162015-120819334

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Abstract:

The field of cavity optomechanics, which concerns the coupling of a mechanical object's motion to the electromagnetic field of a high finesse cavity, allows for exquisitely sensitive measurements of mechanical motion, from large-scale gravitational wave detection to microscale accelerometers. Moreover, it provides a potential means to control and engineer the state of a macroscopic mechanical object at the quantum level, provided one can realize sufficiently strong interaction strengths relative to the ambient thermal noise. Recent experiments utilizing the optomechanical interaction to cool mechanical resonators to their motional quantum ground state allow for a variety of quantum engineering applications, including preparation of non-classical mechanical states and coherent optical to microwave conversion. Optomechanical crystals (OMCs), in which bandgaps for both optical and mechanical waves can be introduced through patterning of a material, provide one particularly attractive means for realizing strong interactions between high-frequency mechanical resonators and near-infrared light. Beyond the usual paradigm of cavity optomechanics involving isolated single mechanical elements, OMCs can also be fashioned into planar circuits for photons and phonons, and arrays of optomechanical elements can be interconnected via optical and acoustic waveguides. Such coupled OMC arrays have been proposed as a way to realize quantum optomechanical memories, nanomechanical circuits for continuous variable quantum information processing and phononic quantum networks, and as a platform for engineering and studying quantum many-body physics of optomechanical meta-materials.

However, while ground state occupancies (that is, average phonon occupancies less than one) have been achieved in OMC cavities utilizing laser cooling techniques, parasitic absorption and the concomitant degradation of the mechanical quality factor fundamentally limit this approach. On the other hand, the high mechanical frequency of these systems allows for the possibility of using a dilution refrigerator to simultaneously achieve low thermal occupancy and long mechanical coherence time by passively cooling the device to the millikelvin regime. This thesis describes efforts to realize the measurement of OMC cavities inside a dilution refrigerator, including the development of fridge-compatible optical coupling schemes and the characterization of the heating dynamics of the mechanical resonator at sub-kelvin temperatures.

We will begin by summarizing the theoretical framework used to describe cavity optomechanical systems, as well as a handful of the quantum applications envisioned for such devices. Then, we will present background on the design of the nanobeam OMC cavities used for this work, along with details of the design and characterization of tapered fiber couplers for optical coupling inside the fridge. Finally, we will present measurements of the devices at fridge base temperatures of T_{f} = 10 mK, using both heterodyne spectroscopy and time-resolved sideband photon counting, as well as detailed analysis of the prospects for future quantum applications based on the observed optically-induced heating.

ID: CaltechTHESIS:03132015-135949868

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Abstract: Researchers have spent decades refining and improving their methods for fabricating smaller, finer-tuned, higher-quality nanoscale optical elements with the goal of making more sensitive and accurate measurements of the world around them using optics. Quantum optics has been a well-established tool of choice in making these increasingly sensitive measurements which have repeatedly pushed the limits on the accuracy of measurement set forth by quantum mechanics. A recent development in quantum optics has been a creative integration of robust, high-quality, and well-established macroscopic experimental systems with highly-engineerable *on-chip* nanoscale oscillators fabricated in cleanrooms. However, merging large systems with nanoscale oscillators often require them to have extremely high aspect-ratios, which make them extremely delicate and difficult to fabricate with an "experimentally reasonable" repeatability, yield and high quality. In this work we give an overview of our research, which focused on microscopic oscillators which are coupled with macroscopic optical cavities towards the goal of cooling them to their motional ground state in room temperature environments. The quality factor of a mechanical resonator is an important figure of merit for various sensing applications and observing quantum behavior. We demonstrated a technique for pushing the quality factor of a micromechanical resonator beyond conventional material and fabrication limits by using an optical field to stiffen and trap a particular motional mode of a nanoscale oscillator. Optical forces increase the oscillation frequency by storing most of the mechanical energy in a nearly loss-less optical potential, thereby strongly diluting the effects of material dissipation. By placing a 130 nm thick SiO_{2} pendulum in an optical standing wave, we achieve an increase in the pendulum center-of-mass frequency from 6.2 to 145 kHz. The corresponding quality factor increases 50-fold from its intrinsic value to a final value of Q_{m} = 5.8(1.1) x 10^{5}, representing more than an order of magnitude improvement over the conventional limits of SiO_{2} for a pendulum geometry. Our technique may enable new opportunities for mechanical sensing and facilitate observations of quantum behavior in this class of mechanical systems. We then give a detailed overview of the techniques used to produce high-aspect-ratio nanostructures with applications in a wide range of quantum optics experiments. The ability to fabricate such nanodevices with high precision opens the door to a vast array of experiments which integrate macroscopic optical setups with lithographically engineered nanodevices. Coupled with atom-trapping experiments in the Kimble Lab, we use these techniques to realize a new waveguide chip designed to address ultra-cold atoms along lithographically patterned nanobeams which have large atom-photon coupling and near 4π Steradian optical access for cooling and trapping atoms. We describe a fully integrated and scalable design where cold atoms are spatially overlapped with the nanostring cavities in order to observe a resonant optical depth of d_{0} ≈ 0.15. The nanodevice illuminates new possibilities for integrating atoms into photonic circuits and engineering quantum states of atoms and light on a microscopic scale. We then describe our work with superconducting microwave resonators coupled to a phononic cavity towards the goal of building an integrated device for quantum-limited microwave-to-optical wavelength conversion. We give an overview of our characterizations of several types of substrates for fabricating a low-loss high-frequency electromechanical system. We describe our electromechanical system fabricated on a Si_{3}N_{4} membrane which consists of a 12 GHz superconducting LC resonator coupled capacitively to the high frequency localized modes of a phononic nanobeam. Using our suspended membrane geometry we isolate our system from substrates with significant loss tangents, drastically reducing the parasitic capacitance of our superconducting circuit to ≈ 2.5$ fF. This opens up a number of possibilities in making a new class of low-loss high-frequency electromechanics with relatively large electromechanical coupling. We present our substrate studies, fabrication methods, and device characterization.

ID: CaltechTHESIS:10292014-120111728

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Abstract:

The topological phases of matter have been a major part of condensed matter physics research since the discovery of the quantum Hall effect in the 1980s. Recently, much of this research has focused on the study of systems of free fermions, such as the integer quantum Hall effect, quantum spin Hall effect, and topological insulator. Though these free fermion systems can play host to a variety of interesting phenomena, the physics of interacting topological phases is even richer. Unfortunately, there is a shortage of theoretical tools that can be used to approach interacting problems. In this thesis I will discuss progress in using two different numerical techniques to study topological phases.

Recently much research in topological phases has focused on phases made up of bosons. Unlike fermions, free bosons form a condensate and so interactions are vital if the bosons are to realize a topological phase. Since these phases are difficult to study, much of our understanding comes from exactly solvable models, such as Kitaev's toric code, as well as Levin-Wen and Walker-Wang models. We may want to study systems for which such exactly solvable models are not available. In this thesis I present a series of models which are not solvable exactly, but which can be studied in sign-free Monte Carlo simulations. The models work by binding charges to point topological defects. They can be used to realize bosonic interacting versions of the quantum Hall effect in 2D and topological insulator in 3D. Effective field theories of "integer" (non-fractionalized) versions of these phases were available in the literature, but our models also allow for the construction of fractional phases. We can measure a number of properties of the bulk and surface of these phases.

Few interacting topological phases have been realized experimentally, but there is one very important exception: the fractional quantum Hall effect (FQHE). Though the fractional quantum Hall effect we discovered over 30 years ago, it can still produce novel phenomena. Of much recent interest is the existence of non-Abelian anyons in FQHE systems. Though it is possible to construct wave functions that realize such particles, whether these wavefunctions are the ground state is a difficult quantitative question that must be answered numerically. In this thesis I describe progress using a density-matrix renormalization group algorithm to study a bilayer system thought to host non-Abelian anyons. We find phase diagrams in terms of experimentally relevant parameters, and also find evidence for a non-Abelian phase known as the "interlayer Pfaffian".

ID: CaltechTHESIS:05282015-205532544

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Abstract:

Quantum mechanics places limits on the minimum energy of a harmonic oscillator via the ever-present "zero-point" fluctuations of the quantum ground state. Through squeezing, however, it is possible to decrease the noise of a single motional quadrature below the zero-point level as long as noise is added to the orthogonal quadrature. While squeezing below the quantum noise level was achieved decades ago with light, quantum squeezing of the motion of a mechanical resonator is a more difficult prospect due to the large thermal occupations of megahertz-frequency mechanical devices even at typical dilution refrigerator temperatures of ~ 10 mK.

Kronwald, Marquardt, and Clerk (2013) propose a method of squeezing a single quadrature of mechanical motion below the level of its zero-point fluctuations, even when the mechanics starts out with a large thermal occupation. The scheme operates under the framework of cavity optomechanics, where an optical or microwave cavity is coupled to the mechanics in order to control and read out the mechanical state. In the proposal, two pump tones are applied to the cavity, each detuned from the cavity resonance by the mechanical frequency. The pump tones establish and couple the mechanics to a squeezed reservoir, producing arbitrarily-large, steady-state squeezing of the mechanical motion. In this dissertation, I describe two experiments related to the implementation of this proposal in an electromechanical system. I also expand on the theory presented in Kronwald et. al. to include the effects of squeezing in the presence of classical microwave noise, and without assumptions of perfect alignment of the pump frequencies.

In the first experiment, we produce a squeezed thermal state using the method of Kronwald et. al.. We perform back-action evading measurements of the mechanical squeezed state in order to probe the noise in both quadratures of the mechanics. Using this method, we detect single-quadrature fluctuations at the level of 1.09 +/- 0.06 times the quantum zero-point motion.

In the second experiment, we measure the spectral noise of the microwave cavity in the presence of the squeezing tones and fit a full model to the spectrum in order to deduce a quadrature variance of 0.80 +/- 0.03 times the zero-point level. These measurements provide the first evidence of quantum squeezing of motion in a mechanical resonator.

ID: CaltechTHESIS:05292015-131603299

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Abstract:

Topological superconductors are particularly interesting in light of the active ongoing experimental efforts for realizing exotic physics such as Majorana zero modes. These systems have excitations with non-Abelian exchange statistics, which provides a path towards topological quantum information processing. Intrinsic topological superconductors are quite rare in nature. However, one can engineer topological superconductivity by inducing effective p-wave pairing in materials which can be grown in the laboratory. One possibility is to induce the proximity effect in topological insulators; another is to use hybrid structures of superconductors and semiconductors.

The proposal of interfacing s-wave superconductors with quantum spin Hall systems provides a promising route to engineered topological superconductivity. Given the exciting recent progress on the fabrication side, identifying experiments that definitively expose the topological superconducting phase (and clearly distinguish it from a trivial state) raises an increasingly important problem. With this goal in mind, we proposed a detection scheme to get an unambiguous signature of topological superconductivity, even in the presence of ordinarily detrimental effects such as thermal fluctuations and quasiparticle poisoning. We considered a Josephson junction built on top of a quantum spin Hall material. This system allows the proximity effect to turn edge states in effective topological superconductors. Such a setup is promising because experimentalists have demonstrated that supercurrents indeed flow through quantum spin Hall edges. To demonstrate the topological nature of the superconducting quantum spin Hall edges, theorists have proposed examining the periodicity of Josephson currents respect to the phase across a Josephson junction. The periodicity of tunneling currents of ground states in a topological superconductor Josephson junction is double that of a conventional Josephson junction. In practice, this modification of periodicity is extremely difficult to observe because noise sources, such as quasiparticle poisoning, wash out the signature of topological superconductors. For this reason, We propose a new, relatively simple DC measurement that can compellingly reveal topological superconductivity in such quantum spin Hall/superconductor heterostructures. More specifically, We develop a general framework for capturing the junction's current-voltage characteristics as a function of applied magnetic flux. Our analysis reveals sharp signatures of topological superconductivity in the field-dependent critical current. These signatures include the presence of multiple critical currents and a non-vanishing critical current for all magnetic field strengths as a reliable identification scheme for topological superconductivity.

This system becomes more interesting as interactions between electrons are involved. By modeling edge states as a Luttinger liquid, we find conductance provides universal signatures to distinguish between normal and topological superconductors. More specifically, we use renormalization group methods to extract universal transport characteristics of superconductor/quantum spin Hall heterostructures where the native edge states serve as a lead. Interestingly, arbitrarily weak interactions induce qualitative changes in the behavior relative to the free-fermion limit, leading to a sharp dichotomy in conductance for the trivial (narrow superconductor) and topological (wide superconductor) cases. Furthermore, we find that strong interactions can in principle induce parafermion excitations at a superconductor/quantum spin Hall junction.

As we identify the existence of topological superconductor, we can take a step further. One can use topological superconductor for realizing Majorana modes by breaking time reversal symmetry. An advantage of 2D topological insulator is that networks required for braiding Majoranas along the edge channels can be obtained by adjoining 2D topological insulator to form corner junctions. Physically cutting quantum wells for this purpose, however, presents technical challenges. For this reason, I propose a more accessible means of forming networks that rely on dynamically manipulating the location of edge states inside of a single 2D topological insulator sheet. In particular, I show that edge states can effectively be dragged into the system's interior by gating a region near the edge into a metallic regime and then removing the resulting gapless carriers via proximity-induced superconductivity. This method allows one to construct rather general quasi-1D networks along which Majorana modes can be exchanged by electrostatic means.

Apart from 2D topological insulators, Majorana fermions can also be generated in other more accessible materials such as semiconductors. Following up on a suggestion by experimentalist Charlie Marcus, I proposed a novel geometry to create Majorana fermions by placing a 2D electron gas in proximity to an interdigitated superconductor-ferromagnet structure. This architecture evades several manufacturing challenges by allowing single-side fabrication and widening the class of 2D electron gas that may be used, such as the surface states of bulk semiconductors. Furthermore, it naturally allows one to trap and manipulate Majorana fermions through the application of currents. Thus, this structure may lead to the development of a circuit that enables fully electrical manipulation of topologically-protected quantum memory. To reveal these exotic Majorana zero modes, I also proposed an interference scheme to detect Majorana fermions that is broadly applicable to any 2D topological superconductor platform.

ID: CaltechTHESIS:06072015-223040119

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Abstract: We present a theoretical study of electronic states in topological insulators with impurities. Chiral edge states in 2d topological insulators and helical surface states in 3d topological insulators show a robust transport against nonmagnetic impurities. Such a nontrivial character inspired physicists to come up with applications such as spintronic devices [1], thermoelectric materials [2], photovoltaics [3], and quantum computation [4]. Not only has it provided new opportunities from a practical point of view, but its theoretical study has deepened the understanding of the topological nature of condensed matter systems. However, experimental realizations of topological insulators have been challenging. For example, a 2d topological insulator fabricated in a HeTe quantum well structure by Konig et al. [5] shows a longitudinal conductance which is not well quantized and varies with temperature. 3d topological insulators such as Bi_{2}Se_{3} and Bi_{2}Te_{3} exhibit not only a signature of surface states, but they also show a bulk conduction [6]. The series of experiments motivated us to study the effects of impurities and coexisting bulk Fermi surface in topological insulators. We first address a single impurity problem in a topological insulator using a semiclassical approach. Then we study the conductance behavior of a disordered topological-metal strip where bulk modes are associated with the transport of edge modes via impurity scattering. We verify that the conduction through a chiral edge channel retains its topological signature, and we discovered that the transmission can be succinctly expressed in a closed form as a ratio of determinants of the bulk Green's function and impurity potentials. We further study the transport of 1d systems which can be decomposed in terms of chiral modes. Lastly, the surface impurity effect on the local density of surface states over layers into the bulk is studied between weak and strong disorder strength limits.

ID: CaltechTHESIS:06022014-093929164

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Abstract:

How powerful are Quantum Computers? Despite the prevailing belief that Quantum Computers are more powerful than their classical counterparts, this remains a conjecture backed by little formal evidence. Shor's famous factoring algorithm [Shor97] gives an example of a problem that can be solved efficiently on a quantum computer with no known efficient classical algorithm. Factoring, however, is unlikely to be NP-Hard, meaning that few unexpected formal consequences would arise, should such a classical algorithm be discovered. Could it then be the case that any quantum algorithm can be simulated efficiently classically? Likewise, could it be the case that Quantum Computers can quickly solve problems much harder than factoring? If so, where does this power come from, and what classical computational resources do we need to solve the hardest problems for which there exist efficient quantum algorithms?

We make progress toward understanding these questions through studying the relationship between classical nondeterminism and quantum computing. In particular, is there a problem that can be solved efficiently on a Quantum Computer that cannot be efficiently solved using nondeterminism? In this thesis we address this problem from the perspective of sampling problems. Namely, we give evidence that approximately sampling the Quantum Fourier Transform of an efficiently computable function, while easy quantumly, is hard for any classical machine in the Polynomial Time Hierarchy. In particular, we prove the existence of a class of distributions that can be sampled efficiently by a Quantum Computer, that likely cannot be approximately sampled in randomized polynomial time with an oracle for the Polynomial Time Hierarchy.

Our work complements and generalizes the evidence given in Aaronson and Arkhipov's work [AA2013] where a different distribution with the same computational properties was given. Our result is more general than theirs, but requires a more powerful quantum sampler.

ID: CaltechTHESIS:05302014-131308138

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Abstract: In this thesis, I will discuss how information-theoretic arguments can be used to produce sharp bounds in the studies of quantum many-body systems. The main advantage of this approach, as opposed to the conventional field-theoretic argument, is that it depends very little on the precise form of the Hamiltonian. The main idea behind this thesis lies on a number of results concerning the structure of quantum states that are conditionally independent. Depending on the application, some of these statements are generalized to quantum states that are approximately conditionally independent. These structures can be readily used in the studies of gapped quantum many-body systems, especially for the ones in two spatial dimensions. A number of rigorous results are derived, including (i) a universal upper bound for a maximal number of topologically protected states that is expressed in terms of the topological entanglement entropy, (ii) a first-order perturbation bound for the topological entanglement entropy that decays superpolynomially with the size of the subsystem, and (iii) a correlation bound between an arbitrary local operator and a topological operator constructed from a set of local reduced density matrices. I also introduce exactly solvable models supported on a three-dimensional lattice that can be used as a reliable quantum memory.

ID: CaltechTHESIS:05102013-172241867

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Abstract: Underlying matter and light are their building blocks of tiny atoms and photons. The ability to control and utilize matter-light interactions down to the elementary single atom and photon level at the nano-scale opens up exciting studies at the frontiers of science with applications in medicine, energy, and information technology. Of these, an intriguing front is the development of quantum networks where N >> 1 single-atom nodes are coherently linked by single photons, forming a collective quantum entity potentially capable of performing quantum computations and simulations. Here, a promising approach is to use optical cavities within the setting of cavity quantum electrodynamics (QED). However, since its first realization in 1992 by Kimble et al., current proof-of-principle experiments have involved just one or two conventional cavities. To move beyond to N >> 1 nodes, in this thesis we investigate a platform born from the marriage of cavity QED and nanophotonics, where single atoms at ~100 nm near the surfaces of lithographically fabricated dielectric photonic devices can strongly interact with single photons, on a chip. Particularly, we experimentally investigate three main types of devices: microtoroidal optical cavities, optical nanofibers, and nanophotonic crystal based structures. With a microtoroidal cavity, we realized a robust and efficient photon router where single photons are extracted from an incident coherent state of light and redirected to a separate output with high efficiency. We achieved strong single atom-photon coupling with atoms located ~100 nm near the surface of a microtoroid, which revealed important aspects in the atom dynamics and QED of these systems including atom-surface interaction effects. We present a method to achieve state-insensitive atom trapping near optical nanofibers, critical in nanophotonic systems where electromagnetic fields are tightly confined. We developed a system that fabricates high quality nanofibers with high controllability, with which we experimentally demonstrate a state-insensitive atom trap. We present initial investigations on nanophotonic crystal based structures as a platform for strong atom-photon interactions. The experimental advances and theoretical investigations carried out in this thesis provide a framework for and open the door to strong single atom-photon interactions using nanophotonics for chip-integrated quantum networks.

ID: CaltechTHESIS:06042013-123144999

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Abstract:

This thesis addresses whether it is possible to build a robust memory device for quantum information. Many schemes for fault-tolerant quantum information processing have been developed so far, one of which, called topological quantum computation, makes use of degrees of freedom that are inherently insensitive to local errors. However, this scheme is not so reliable against thermal errors. Other fault-tolerant schemes achieve better reliability through active error correction, but incur a substantial overhead cost. Thus, it is of practical importance and theoretical interest to design and assess fault-tolerant schemes that work well at finite temperature without active error correction.

In this thesis, a three-dimensional gapped lattice spin model is found which demonstrates for the first time that a reliable quantum memory at finite temperature is possible, at least to some extent. When quantum information is encoded into a highly entangled ground state of this model and subjected to thermal errors, the errors remain easily correctable for a long time without any active intervention, because a macroscopic energy barrier keeps the errors well localized. As a result, stored quantum information can be retrieved faithfully for a memory time which grows exponentially with the square of the inverse temperature. In contrast, for previously known types of topological quantum storage in three or fewer spatial dimensions the memory time scales exponentially with the inverse temperature, rather than its square.

This spin model exhibits a previously unexpected topological quantum order, in which ground states are locally indistinguishable, pointlike excitations are immobile, and the immobility is not affected by small perturbations of the Hamiltonian. The degeneracy of the ground state, though also insensitive to perturbations, is a complicated number-theoretic function of the system size, and the system bifurcates into multiple noninteracting copies of itself under real-space renormalization group transformations. The degeneracy, the excitations, and the renormalization group flow can be analyzed using a framework that exploits the spin model's symmetry and some associated free resolutions of modules over polynomial algebras.

ID: CaltechTHESIS:05292013-140541902

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Abstract:

The field of cavity-optomechanics explores the interaction of light with sound in an ever increasing array of devices. This interaction allows the mechanical system to be both sensed and controlled by the optical system, opening up a wide variety of experiments including the cooling of the mechanical resonator to its quantum mechanical ground state and the squeezing of the optical field upon interaction with the mechanical resonator, to name two.

In this work we explore two very different systems with different types of optomechanical coupling. The first system consists of two microdisk optical resonators stacked on top of each other and separated by a very small slot. The interaction of the disks causes their optical resonance frequencies to be extremely sensitive to the gap between the disks. By careful control of the gap between the disks, the optomechanical coupling can be made to be quadratic to first order which is uncommon in optomechanical systems. With this quadratic coupling the light field is now sensitive to the energy of the mechanical resonator and can directly control the potential energy trapping the mechanical motion. This ability to directly control the spring constant without modifying the energy of the mechanical system, unlike in linear optomechanical coupling, is explored.

Next, the bulk of this thesis deals with a high mechanical frequency optomechanical crystal which is used to coherently convert photons between different frequencies. This is accomplished via the engineered linear optomechanical coupling in these devices. Both classical and quantum systems utilize the interaction of light and matter across a wide range of energies. These systems are often not naturally compatible with one another and require a means of converting photons of dissimilar wavelengths to combine and exploit their different strengths. Here we theoretically propose and experimentally demonstrate coherent wavelength conversion of optical photons using photon-phonon translation in a cavity-optomechanical system. For an engineered silicon optomechanical crystal nanocavity supporting a 4 GHz localized phonon mode, optical signals in a 1.5 MHz bandwidth are coherently converted over a 11.2 THz frequency span between one cavity mode at wavelength 1460 nm and a second cavity mode at 1545 nm with a 93% internal (2% external) peak efficiency. The thermal and quantum limiting noise involved in the conversion process is also analyzed and, in terms of an equivalent photon number signal level, are found to correspond to an internal noise level of only 6 and 4 times 10x^-3 quanta, respectively.

We begin by developing the requisite theoretical background to describe the system. A significant amount of time is then spent describing the fabrication of these silicon nanobeams, with an emphasis on understanding the specifics and motivation. The experimental demonstration of wavelength conversion is then described and analyzed. It is determined that the method of getting photons into the cavity and collected from the cavity is a fundamental limiting factor in the overall efficiency. Finally, a new coupling scheme is designed, fabricated, and tested that provides a means of coupling greater than 90% of photons into and out of the cavity, addressing one of the largest obstacles with the initial wavelength conversion experiment.

ID: CaltechTHESIS:05312013-144103500

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Abstract:

Optical frequency combs (OFCs) provide direct phase-coherent link between optical and RF frequencies, and enable precision measurement of optical frequencies. In recent years, a new class of frequency combs (microcombs) have emerged based on parametric frequency conversions in dielectric microresonators. Micocombs have large line spacing from 10's to 100's GHz, allowing easy access to individual comb lines for arbitrary waveform synthesis. They also provide broadband parametric gain bandwidth, not limited by specific atomic or molecular transitions in conventional OFCs. The emerging applications of microcombs include low noise microwave generation, astronomical spectrograph calibration, direct comb spectroscopy, and high capacity telecommunications.

In this thesis, research is presented starting with the introduction of a new type of chemically etched, planar silica-on-silicon disk resonator. A record Q factor of 875 million is achieved for on-chip devices. A simple and accurate approach to characterize the FSR and dispersion of microcavities is demonstrated. Microresonator-based frequency combs (microcombs) are demonstrated with microwave repetition rate less than 80 GHz on a chip for the first time. Overall low threshold power (as low as 1 mW) of microcombs across a wide range of resonator FSRs from 2.6 to 220 GHz in surface-loss-limited disk resonators is demonstrated. The rich and complex dynamics of microcomb RF noise are studied. High-coherence, RF phase-locking of microcombs is demonstrated where injection locking of the subcomb offset frequencies are observed by pump-detuning-alignment. Moreover, temporal mode locking, featuring subpicosecond pulses from a parametric 22 GHz microcomb, is observed. We further demonstrated a shot-noise-limited white phase noise of microcomb for the first time. Finally, stabilization of the microcomb repetition rate is realized by phase lock loop control.

For another major nonlinear optical application of disk resonators, highly coherent, simulated Brillouin lasers (SBL) on silicon are also demonstrated, with record low Schawlow-Townes noise less than 0.1 Hz^2/Hz for any chip-based lasers and low technical noise comparable to commercial narrow-linewidth fiber lasers. The SBL devices are efficient, featuring more than 90% quantum efficiency and threshold as low as 60 microwatts. Moreover, novel properties of the SBL are studied, including cascaded operation, threshold tuning, and mode-pulling phenomena. Furthermore, high performance microwave generation using on-chip cascaded Brillouin oscillation is demonstrated. It is also robust enough to enable incorporation as the optical voltage-controlled-oscillator in the first demonstration of a photonic-based, microwave frequency synthesizer. Finally, applications of microresonators as frequency reference cavities and low-phase-noise optomechanical oscillators are presented.

ID: CaltechTHESIS:05312013-151745220

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Abstract:

Quantum computing offers powerful new techniques for speeding up the calculation of many classically intractable problems. Quantum algorithms can allow for the efficient simulation of physical systems, with applications to basic research, chemical modeling, and drug discovery; other algorithms have important implications for cryptography and internet security.

At the same time, building a quantum computer is a daunting task, requiring the coherent manipulation of systems with many quantum degrees of freedom while preventing environmental noise from interacting too strongly with the system. Fortunately, we know that, under reasonable assumptions, we can use the techniques of quantum error correction and fault tolerance to achieve an arbitrary reduction in the noise level.

In this thesis, we look at how additional information about the structure of noise, or "noise bias," can improve or alter the performance of techniques in quantum error correction and fault tolerance. In Chapter 2, we explore the possibility of designing certain quantum gates to be extremely robust with respect to errors in their operation. This naturally leads to structured noise where certain gates can be implemented in a protected manner, allowing the user to focus their protection on the noisier unprotected operations.

In Chapter 3, we examine how to tailor error-correcting codes and fault-tolerant quantum circuits in the presence of dephasing biased noise, where dephasing errors are far more common than bit-flip errors. By using an appropriately asymmetric code, we demonstrate the ability to improve the amount of error reduction and decrease the physical resources required for error correction.

In Chapter 4, we analyze a variety of protocols for distilling magic states, which enable universal quantum computation, in the presence of faulty Clifford operations. Here again there is a hierarchy of noise levels, with a fixed error rate for faulty gates, and a second rate for errors in the distilled states which decreases as the states are distilled to better quality. The interplay of of these different rates sets limits on the achievable distillation and how quickly states converge to that limit.

ID: CaltechTHESIS:05302013-143644943

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Abstract:

Mechanical resonators are the most basic and ubiquitous physical systems known. In on-chip form, they are used to process high frequency signals in every cell phone, television, and laptop. They have also been in the last few decades in different shapes and forms, a critical part of progress in quantum information sciences with kilogram-scale mirrors for gravitational wave detection measuring motion at its quantum limits, and the motion of single ions being used to link qubits for quantum computation.

Optomechanics is a field primarily concerned with coupling light to the motion of mechanical structures. This thesis contains descriptions of recent work with mechanical systems in the megahertz to gigahertz frequency range, formed by nanofabricating novel photonic/phononic structures on a silicon chip. These structures are designed to have both optical and mechanical resonances, and laser light is used to address and manipulate their motional degrees of freedom through radiation pressure forces. We laser cool these mechanical resonators to their ground states, and observe for the first time the quantum zero-point motion of a nanomechanical resonator. Conversely, we show that engineered mechanical resonances drastically modify the optical response of our structures, creating large effective optical nonlinearities not present in bulk silicon. We experimentally demonstrate aspects of these nonlinearities by proposing and observing ``electromagnetically induced transparency'' and light slowed down to 6 m/s, as well as wavelength conversion, and generation of nonclassical optical radiation. Finally, the application of optomechanics to longstanding problems in quantum and classical communications are proposed and investigated.

ID: CaltechTHESIS:05312013-145253965

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Abstract:

This thesis details the investigations of the unconventional low-energy quasiparticle excitations in electron-type cuprate superconductors and electron-type ferrous superconductors as well as the electronic properties of Dirac fermions in graphene and three-dimensional strong topological insulators through experimental studies using spatially resolved scanning tunneling spectroscopy (STS) experiments.

Magnetic-field- and temperature-dependent evolution of the spatially resolved quasiparticle spectra in the electron-type cuprate La_{0.1}Sr_{0.9}CuO_{2} (La-112) T_{C} = 43 K, are investigated experimentally. For temperature (T) less than the superconducting transition temperature (TC), and in zero field, the quasiparticle spectra of La-112 exhibits gapped behavior with two coherence peaks and no satellite features. For magnetic field measurements at T < TC, first ever observation of vortices in La-112 are reported. Moreover, pseudogap-like spectra are revealed inside the core of vortices, where superconductivity is suppressed. The intra-vortex pseudogap-like spectra are characterized by an energy gap of V_{PG} = 8.5 ± 0.6 meV, while the inter-vortex quasiparticle spectra shows larger peak-to-peak gap values characterized by Δ_{pk-pk}(H) >V_{PG}, and Δ_{pk-pk} (0)=12.2 ± 0.8 meV > Δ_{pk-pk} (H > 0). The quasiparticle spectra are found to be gapped at all locations up to the highest magnetic field examined (H = 6T) and reveal an apparent low-energy cutoff at the V_{PG} energy scale.

Magnetic-field- and temperature-dependent evolution of the spatially resolved quasiparticle spectra in the electron-type "122" iron-based Ba(Fe_{1-x}Co_{x})_{2}A_{s2} are investigated for multiple doping levels (x = 0.06, 0.08, 0.12 with T_{C}= 14 K, 24 K, and 20 K). For all doping levels and the T < T_{C}, two-gap superconductivity is observed. Both superconducting gaps decrease monotonically in size with increasing temperature and disappear for temperatures above the superconducting transition temperature, T_{C}. Magnetic resonant modes that follow the temperature dependence of the superconducting gaps have been identified in the tunneling quasiparticle spectra. Together with quasiparticle interference (QPI) analysis and magnetic field studies, this provides strong evidence for two-gap sign-changing s-wave superconductivity.

Additionally spatial scanning tunneling spectroscopic studies are performed on mechanically exfoliated graphene and chemical vapor deposition grown graphene. In all cases lattice strain exerts a strong influence on the electronic properties of the sample. In particular topological defects give rise to pseudomagnetic fields (B ~ 50 Tesla) and charging effects resulting in quantized conductance peaks associated with the integer and fractional Quantum Hall States.

Finally, spectroscopic studies on the 3D-STI, Bi_{2}Se_{3} found evidence of impurity resonance in the surface state. The impurities are in the unitary limit and the spectral resonances are localized spatially to within ~ 0.2 nm of the impurity. The spectral weight of the impurity resonance diverges as the Fermi energy approaches the Dirac point and the rapid recovery of the surface state suggests robust topological protection against perturbations that preserve time reversal symmetry.

ID: CaltechTHESIS:05142013-151159910

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Abstract:

Disorder and interactions both play crucial roles in quantum transport. Decades ago, Mott showed that electron-electron interactions can lead to insulating behavior in materials that conventional band theory predicts to be conducting. Soon thereafter, Anderson demonstrated that disorder can localize a quantum particle through the wave interference phenomenon of Anderson localization. Although interactions and disorder both separately induce insulating behavior, the interplay of these two ingredients is subtle and often leads to surprising behavior at the periphery of our current understanding. Modern experiments probe these phenomena in a variety of contexts (e.g. disordered superconductors, cold atoms, photonic waveguides, etc.); thus, theoretical and numerical advancements are urgently needed. In this thesis, we report progress on understanding two contexts in which the interplay of disorder and interactions is especially important.

The first is the so-called “dirty” or random boson problem. In the past decade, a strong-disorder renormalization group (SDRG) treatment by Altman, Kafri, Polkovnikov, and Refael has raised the possibility of a new unstable fixed point governing the superfluid-insulator transition in the one-dimensional dirty boson problem. This new critical behavior may take over from the weak-disorder criticality of Giamarchi and Schulz when disorder is sufficiently strong. We analytically determine the scaling of the superfluid susceptibility at the strong-disorder fixed point and connect our analysis to recent Monte Carlo simulations by Hrahsheh and Vojta. We then shift our attention to two dimensions and use a numerical implementation of the SDRG to locate the fixed point governing the superfluid-insulator transition there. We identify several universal properties of this transition, which are fully independent of the microscopic features of the disorder.

The second focus of this thesis is the interplay of localization and interactions in systems with high energy density (i.e., far from the usual low energy limit of condensed matter physics). Recent theoretical and numerical work indicates that localization can survive in this regime, provided that interactions are sufficiently weak. Stronger interactions can destroy localization, leading to a so-called many-body localization transition. This dynamical phase transition is relevant to questions of thermalization in isolated quantum systems: it separates a many-body localized phase, in which localization prevents transport and thermalization, from a conducting (“ergodic”) phase in which the usual assumptions of quantum statistical mechanics hold. Here, we present evidence that many-body localization also occurs in quasiperiodic systems that lack true disorder.

ID: CaltechTHESIS:05292013-170142035

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Abstract:

The theories of relativity and quantum mechanics, the two most important physics discoveries of the 20th century, not only revolutionized our understanding of the nature of space-time and the way matter exists and interacts, but also became the building blocks of what we currently know as modern physics. My thesis studies both subjects in great depths --- this intersection takes place in gravitational-wave physics.

Gravitational waves are "ripples of space-time", long predicted by general relativity. Although indirect evidence of gravitational waves has been discovered from observations of binary pulsars, direct detection of these waves is still actively being pursued. An international array of laser interferometer gravitational-wave detectors has been constructed in the past decade, and a first generation of these detectors has taken several years of data without a discovery. At this moment, these detectors are being upgraded into second-generation configurations, which will have ten times better sensitivity. Kilogram-scale test masses of these detectors, highly isolated from the environment, are probed continuously by photons. The sensitivity of such a quantum measurement can often be limited by the Heisenberg Uncertainty Principle, and during such a measurement, the test masses can be viewed as evolving through a sequence of nearly pure quantum states.

The first part of this thesis (Chapter 2) concerns how to minimize the adverse effect of thermal fluctuations on the sensitivity of advanced gravitational detectors, thereby making them closer to being quantum-limited. My colleagues and I present a detailed analysis of coating thermal noise in advanced gravitational-wave detectors, which is the dominant noise source of Advanced LIGO in the middle of the detection frequency band. We identified the two elastic loss angles, clarified the different components of the coating Brownian noise, and obtained their cross spectral densities.

The second part of this thesis (Chapters 3-7) concerns formulating experimental concepts and analyzing experimental results that demonstrate the quantum mechanical behavior of macroscopic objects - as well as developing theoretical tools for analyzing quantum measurement processes. In Chapter 3, we study the open quantum dynamics of optomechanical experiments in which a single photon strongly influences the quantum state of a mechanical object. We also explain how to engineer the mechanical oscillator's quantum state by modifying the single photon's wave function.

In Chapters 4-5, we build theoretical tools for analyzing the so-called "non-Markovian" quantum measurement processes. Chapter 4 establishes a mathematical formalism that describes the evolution of a quantum system (the plant), which is coupled to a non-Markovian bath (i.e., one with a memory) while at the same time being under continuous quantum measurement (by the probe field). This aims at providing a general framework for analyzing a large class of non-Markovian measurement processes. Chapter 5 develops a way of characterizing the non-Markovianity of a bath (i.e.,whether and to what extent the bath remembers information about the plant) by perturbing the plant and watching for changes in the its subsequent evolution. Chapter 6 re-analyzes a recent measurement of a mechanical oscillator's zero-point fluctuations, revealing nontrivial correlation between the measurement device's sensing noise and the quantum rack-action noise.

Chapter 7 describes a model in which gravity is classical and matter motions are quantized, elaborating how the quantum motions of matter are affected by the fact that gravity is classical. It offers an experimentally plausible way to test this model (hence the nature of gravity) by measuring the center-of-mass motion of a macroscopic object.

The most promising gravitational waves for direct detection are those emitted from highly energetic astrophysical processes, sometimes involving black holes - a type of object predicted by general relativity whose properties depend highly on the strong-field regime of the theory. Although black holes have been inferred to exist at centers of galaxies and in certain so-called X-ray binary objects, detecting gravitational waves emitted by systems containing black holes will offer a much more direct way of observing black holes, providing unprecedented details of space-time geometry in the black-holes' strong-field region.

The third part of this thesis (Chapters 8-11) studies black-hole physics in connection with gravitational-wave detection.

Chapter 8 applies black hole perturbation theory to model the dynamics of a light compact object orbiting around a massive central Schwarzschild black hole. In this chapter, we present a Hamiltonian formalism in which the low-mass object and the metric perturbations of the background spacetime are jointly evolved. Chapter 9 uses WKB techniques to analyze oscillation modes (quasi-normal modes or QNMs) of spinning black holes. We obtain analytical approximations to the spectrum of the weakly-damped QNMs, with relative error O(1/L^2), and connect these frequencies to geometrical features of spherical photon orbits in Kerr spacetime. Chapter 11 focuses mainly on near-extremal Kerr black holes, we discuss a bifurcation in their QNM spectra for certain ranges of (l,m) (the angular quantum numbers) as a/M → 1. With tools prepared in Chapter 9 and 10, in Chapter 11 we obtain an analytical approximate for the scalar Green function in Kerr spacetime.

ID: CaltechTHESIS:05222013-233805938

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Abstract:

Compared to fiber optic systems, on-chip optical devices provide reasonable optical performance and mechanical stability in a smaller footprint and at a lower cost. Such devices, including resonators and waveguides, have been applied in diverse areas of scientific research, including quantum information, nonlinear optics, cavity optomechanics, telecommunications, biodetection, rotation sensing, high stability microwave oscillators, and all-optical signal processing. As performance demands on these applications increase, resonators and waveguides with ultralow propagation loss become critical.

In this thesis, we first demonstrate a new resonator with a record Q factor of 875 million for on-chip devices. The fabrication of our device avoids the requirement for a specialized processing step, which in microtoroid resonators has made it difficult to control their size and achieve millimeter- and centimeter-scale diameters. Attaining these sizes is important in applications such as microcombs. The resonators not only set a new benchmark for the Q factor on a chip, but also provide, for the first time, full compatibility of this important device class with conventional semiconductor processing.

Meanwhile, we demonstrate a monolithic waveguide as long as 27 m (39 m optical path length), and featuring broadband loss rate values of (0.08 ± 0.01) dB/m measured over 7 m by optical backscattering. Resonator measurements show a further reduction of loss to 0.037 dB/m, close to that of optical fibers when first considered a viable technology. Scaling this waveguide to integrated spans exceeding 250 m and attenuation rates below 0.01 dB/m is discussed. This chip-based waveguide and resonator improve shock resistance, and afford the possibility of integration for system-on-a chip functionality.

We finally demonstrate a highly sensitive nanoparticle and virus detection method by using a thermal-stabilized reference interferometer in conjunction with an ultrahigh-Q microcavity. Sensitivity is sufficient to resolve shifts caused by binding of individual nanobeads in solution down to a record radius of 12.5 nm, a size approaching that of single protein molecules. A histogram of wavelength shift versus nanoparticle radius shows that particle size can be inferred from shift maxima.

ID: CaltechTHESIS:02072013-163825736

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Abstract:

There has been a barrage of interest in recent years to marry the fields of nanomechanics and quantum optics. Mechanical systems provide sensitive and scalable architectures for sensing applications ranging from atomic force microscopy to gravity wave interferometry. Optical resonators driven by low noise lasers provide a quiet and well-understood means to read-out and manipulate mechanical motion, by way of the radiation pressure force. Taken to an extreme, a device consisting of a high-Q nanomechanical oscillator coupled to a high-finesse optical cavity may enable ground-state preparation of the mechanical element, thus paving the way for a new class of quantum technology based on chip-scale phononic devices coupled to optical photons. By way of mutual coupling to the optical field, this architecture may enable coupling of single phonons to real or artificial atoms, an enticing prospect because of the vast "quantum optics toolbox" already developed for cavity quantum electrodynamics.

The first step towards these goals --- ground-state cooling of the mechanical element in a "cavity optomechanical" system --- has very recently been realized in a cryogenic setup. The work presented in this thesis describes an effort to extend this capability to a room temperature apparatus, so that the usual panoply of table-top optical/atomic physics tools can be brought to bear. This requires a mechanical oscillator with exceptionally low dissipation, as well as careful attention to extraneous sources of noise in both the optical and mechanical componentry. Our particular system is based on a high-Q, high-stress silicon nitride membrane coupled to a high-finesse Fabry-Perot cavity. The purpose of this thesis is to record in detail the procedure for characterizing/modeling the physical properties of the membrane resonator, the optical cavity, and their mutual interaction, as well as extraneous sources of noise related to multimode thermal motion of the oscillator, thermal motion of the cavity apparatus, optical absorption, and laser phase fluctuations. Our principle experimental result is the radiation pressure-based cooling of a high order, 4.8 MHz drum mode of the membrane from room temperature to ~ 100 mK (~ 500 phonons). Secondary results include an investigation of the Q-factor of membrane oscillators with various geometries, some of which exhibit state-of-the-art Q x frequency products of 3 x 10^13 Hz, and a novel technique to suppress extraneous radiation pressure noise using electro-optic feedback.

ID: CaltechTHESIS:06122012-123343193

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Abstract:

The recent experimental realizations of spin-1/2 gapless quantum spin liquids in two-dimensional triangular lattice organic compounds EtMe_{3}Sb[Pd(dmit)_{2}]_{2} and κ-(ET)_{2}Cu_{2}(CN)_{3} have stimulated the investigation of the gapless spin liquid theories. The models in dimensions greater than one (D>1) usually involve multispin interactions, such as ring exchange interactions, that are difficult to study, while effective gauge theory descriptions are not well-controlled to give reliable physics information. Driven by the need for a systematic and controlled analysis of such phase, such models on ladders are seriously studied. This thesis first focuses on such ladder models. We propose that the gapless spin liquid phase can be accessed from a two-band interacting electron model by metal-Mott insulator phase transition. We use Bosonization analysis and weak-coupling Renormalization Group to further study the gapless spin liquid state in the presence of Zeeman magnetic fields or orbital magnetic fields. Several new exotic gapless spin liquids with dominant spin nematic correlations are predicted. In such a ladder spin liquid, we also consider the impurity effects. We conclude that the local energy textures and oscillating spin susceptibilities around the impurities are nontrivial and can be observed in the experiments. We then shift our focus to another theoretical candidate, an SU(2)-invariant spin liquid with Majorana excitations, which can also qualitatively explain the experimental phenomenology. We construct an exactly solvable Kitaev-type model realizing the long-wavelength Majorana spin liquid state and study its properties. We find that the state has equal power-law spin and spin-nematic correlations and behaves nontrivially in the presence of Zeeman magnetic fields. Finally, we realize such Majorana spin liquid states on a two-leg ladder and further explore their stability. We conclude the states can be stable against short-range interactions and gauge field fluctuations.

ID: CaltechTHESIS:05142012-220503327

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Abstract:

Quantum mechanics continues to intrigue us with bizarre predictions that seemingly run counter to our everyday classical intuition. Superposition, zero-point motion, entanglement, and inescapable bounds on measurement precision are just a few purely quantum mechanical effects that come to mind. The promise of observing such effects in mesoscale mechanical resonators some orders of magnitude larger than the systems these effects had once been confined to, has resulted in surging interest in the field of cavity electro- and optomechanics. In these systems, the strong interaction of light and matter allows radiation pressure forces to provide significant damping to the mechanical motion, and serves as a means to mitigate the quantum-destroying, decohering effects of the pervasive thermal bath. However, for this backaction cooling to reduce the phonon occupation of a mechanical mode below unity, the confluence of the device and experimental setup must conform to a very strict set of conditions characterized by high optical and mechanical cavity quality factors, low optical absorption, low drive noise, and sufficiently sensitive detection.

In this work, we describe the first optomechanical device and all-optical experimental setup to simultaneously satisfy these conditions, realizing the quantum ground state cooling of a 3.7 GHz mechanical mode (with a final phonon occupation of 0.85 +/- 0.08) in a picogram and micron-scale patterned nanobeam structure from a bath temperature of approximately 20 K. In context, subunity occupation of a mechanical mode in a similar-sized object had previously only been achieved by electromechanical devices operating in millikelvin dilution refrigerator environments. We also discuss the numerical simulation efforts involved in designing and optimizing these novel, coupled optical and mechanical resonators, and the fabrication procedure to realize them in silicon microchips. We recognize that this cooling result represents only an initial step toward the complete optical control of mesoscale mechanical oscillators in the quantum regime. To this end, we summarize an experiment we performed to detect the quantum zero-point motion of a nanobeam via scattering sideband asymmetry. We further show work in improving the optomechanical coupling and quality factors of these devices, as well as devising more efficient coupling schemes to improve measurement sensitivity.

ID: CaltechTHESIS:05302012-124605570

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