CaltechDATA: Monograph
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A Caltech Library Repository Feedhttp://www.rssboard.org/rss-specificationpython-feedgenenThu, 28 Mar 2024 11:12:29 -0700Scanning Tunneling Spectroscopy Studies of High-Temperature Cuprate Superconductors
https://resolver.caltech.edu/CaltechETD:etd-05222006-124257
Year: 2006
DOI: 10.7907/11FP-3M88
<p>This thesis presents the scanning tunneling spectroscopic studies of the non-universal electronic properties among electron- and hole-doped cuprates. Tunneling spectra of the electron-doped Sr0.9La0.1CuO2 and the hole-doped YBa2Cu3O6+delta reveal distinctly different behavior in the pairing symmetries, pseudogap phenomena, satellite features, and low-energy excitations. While underdoped and optimally doped YBa2Cu3O6+delta exhibits d-wave and overdoped Ca-doped YBa2Cu3O6+delta (d+s)-wave pairing symmetry, the electron-doped Sr0.9La0.1CuO2 shows fully gapped s-wave pairing symmetry. The absence of the satellite features and pseudogap in tunneling spectra of electron-doped cuprates sharply contrasts with their general presence in hole-doped cuprates. Furthermore, the subgap low-energy spectral characteristics of Sr0.9La0.1CuO2 deviate substantially from the mean-field Bardeen-Cooper-Schrieffer theory, while those of YBa2Cu3O6+delta can be fully accounted for by the mean-field generalized Blonder-Tinkham-Klapwijk formalism.</p>
<p>Despite the aforementioned disparities, several experimental results reveal important connections between the two types of cuprates. For instance, the coexistence of the pseudogap and superconducting spectra in hole-doped cuprates and the observations of the current- and field-induced pseudogap in electron-doped cuprates suggest that competing orders, manifested as the pseudogap, coexist with superconductivity in both types of cuprates. In addition, by comparing the tunneling spectra with the high-field vortex dynamics measurements, we find that the quasiparticle spectral characteristics of Sr0.9La0.1CuO2 and YBa2Cu3O6+delta correlate with the degree of field-induced quantum phase fluctuations of the two compounds.</p>
<p>Based on these findings, we propose a simple model of coexisting density waves with superconductivity to unify the apparent non-universal phenomena among cuprate superconductors. By incorporating quantum phase fluctuations and adopting realistic band structures, numerical simulations of the quasiparticle tunneling spectra demonstrate excess subgap low-energy excitations, which is consistent with the empirical observations in Sr0.9La0.1CuO2. Furthermore, by tuning the ratio of the density waves to superconductivity, the theoretical calculations reproduce the absence of pseudogap phenomena in electron-doped cuprates and the general presence of he pseudogap in hole-doped cuprates. Thereby, we conclude that the competing orders that coexist with superconductivity in cuprate superconductors contribute to the rich cuprate phenomenology.</p>https://resolver.caltech.edu/CaltechETD:etd-05222006-124257Experiments on the Self-Organized Critical State of ⁴He
https://resolver.caltech.edu/CaltechETD:etd-06062006-094705
Year: 2006
DOI: 10.7907/NN9C-1A08
<p>When a heat flux is applied downwards through a sample of ⁴He near the superfluid transition temperature T<sub>λ</sub>, the gradient in the temperature self-organizes to the gradient in T<sub>λ</sub> caused by gravity. This creates the Self-Organized Critical (SOC) state. Previous experiments have observed the state, measured the self-organization temperature T<sub>SOC</sub> vs. heat flux, and investigated a remarkable wave that only travels upwards against the flow of the heat flux.</p>
<p>We report the first results of the heat capacity of the SOC state, C<sub>∇T</sub>, for heat fluxes 60 nW/cm² < Q < 13 uW/cm² and corresponding temperatures 9 nK > T<sub>SOC</sub>-T<sub>λ</sub> > -1.1 uK. We find that C<sub>∇T</sub> tracks the static (i.e., zero heat flux) unrounded (i.e., in zero gravity) heat capacity C_0 with two exceptions. The first is that within 250 nK of T<sub>λ</sub>, C_gradT is depressed relative to C₀ and the maximum in C<sub>∇T</sub> is shifted to 50 nK below T<sub>λ</sub>. The second difference is that at high heat flux, C<sub>∇T</sub> is again depressed relative to C₀ with the departure starting at about 650 nK below T<sub>λ</sub>.</p>
<p>We present the most extensive measurements of the speed and attenuation of the SOC wave to date. We report wave speed measurements taken over our full experimental range 30 nW/cm² < Q < 13 uW/cm² and attenuation results over the limited range that produced enough attenuation to measure. We also report the first accurate calculation of the speed of the SOC wave.</p>https://resolver.caltech.edu/CaltechETD:etd-06062006-094705All-Optical Spinor Bose-Einstein Condensation and the Spinor Dynamics-Driven Atom Laser
https://resolver.caltech.edu/CaltechETD:etd-05242006-104400
Year: 2006
DOI: 10.7907/WEVF-9991
<p>Optical trapping as a viable means of exploring the physics of ultracold dilute atomic gases has revealed a new spectrum of physical phenomena. In particular, macroscopic and sudden occupation of the ground state below a critical temperature—-a phenomenon known as Bose-Einstein condensation—-has become an even richer system for the study of quantum mechanics, ultracold collisions, and many-body physics in general. Optical trapping liberates the spin degree of the BEC, making the order parameter vectorial (‘spinor BEC’), as opposed to the scalar order of traditional magnetically trapped condensates.</p>
<p>The work described within is divided into two main efforts. The first encompasses the all-optical creation of a Bose-Einstein condensate in rubidium vapor. An all-optical path to spinor BEC (as opposed to transfer to an optical trap from a magnetic-trap condensate) was desired both for the simplicity of the experimental setup and also for the potential gains in speed of creation; evaporative cooling, the only known path to dilute-gas condensation, works only as efficiently as the rate of elastic collisions in the gas, a rate that starts out much higher in optical traps. The first all-optical BEC was formed elsewhere in 2001; the years following saw many groups worldwide seeking to create their own version. Our own all-optical spinor BEC, made with a single-beam dipole trap formed by a focused CO₂ laser, is described here, with particular attention paid to trap loading, measurement of trap parameters, and the use of a novel 780 nm high-power laser system.</p>
<p>The second part describes initial experiments performed with the nascent condensate. The spinor properties of the condensate are documented, and a measurement is made of the density-dependent rate of spin mixing in the condensate. In addition, we demonstrate a novel dual-beam atom laser formed by outcoupling oppositely polarized components of the condensate, whose populations have been coherently evolved through spin dynamics. We drive coherent spin-mixing evolution through adiabatic compression of the initially weak trap. Such dual beams, nominally number-correlated through the angular momentum-conserving collision m=0 + m=0 ⇌ m=+1 + m=-1 have been proposed as tools to explore entanglement and squeezing in Bose-Einstein condensates.</p>https://resolver.caltech.edu/CaltechETD:etd-05242006-104400Rotating Rayleigh-Bénard Convection
https://resolver.caltech.edu/CaltechETD:etd-08252006-154116
Year: 2007
DOI: 10.7907/961N-6776
<p>Rotating Rayleigh-Benard convection (rRBC) is studied as a paradigmatic example of pattern formation and spatiotemporal chaos. For large enough rotation rates, this system undergoes a supercritical bifurcation from the uniform state to a state known as domain chaos.</p>
<p>In domain chaos, domains of straight parallel rolls change their orientation and size discretely. This roll switching causes an overall counterclockwise precession of the pattern. An additional mechanism of precession, glide-induced precession, is introduced here, by deriving the rRBC amplitude equation to higher order. New terms due to the rotation cause rolls to precess whenever there is an amplitude gradient in the direction parallel to the rolls. Hence, dislocations which are stationary in a nonrotating system will glide in a rotating frame, causing the overall precession.</p>
<p>Theory that includes the Coriolis force but ignores the centrifugal force predicted scaling laws near the transition to domain chaos. However, experimenters found different scaling laws. The scaling laws are studied here by direct numerical simulations (DNS) for the exact parameters as experiments. When only the Coriolis force is included, the DNS scaling laws agree with theory. When the centrifugal force is also included, the DNS scaling laws agree better with experiment; hence the centrifugal force cannot be neglected from theory.</p>
<p>The coefficients of the amplitude equation for the Complex Ginzburg-Landau equation (CGLE) are found for DNS of traveling waves. They agree well with experimental results. The CGLE is chaotic for certain values of the coefficients. However, for the parameters in the DNS, those chaotic regimes were not realized.</p>
<p>Leading order Lyapunov exponents (LLE) and eigenvectors are computed for both rotating and nonrotating convection. For certain parameters, these systems are found to have positive LLEs; hence they are truly chaotic. For time-dependent systems, the leading eigenvector is characterized by localized bursts of activity which are associated with dynamical events. The short-time dynamics of the LLE is correlated with these dynamical events. However, contributions to the LLE are due to non-periodic events only.</p>
<p>Lagrangian particle tracking methods are employed for rRBC. These systems exhibit chaotic advection in that initially localized particle trajectories explore the available phase space.</p>https://resolver.caltech.edu/CaltechETD:etd-08252006-154116Continuous Quantum Measurement of Cold Alkali-Atom Spins
https://resolver.caltech.edu/CaltechETD:etd-02172007-172548
Year: 2007
DOI: 10.7907/7PTX-AB16
<p>The field of quantum metrology concerns the physical measurement of sensors with a precision comparable to fundamental limits set by quantum mechanics. It is possible to outperform naive interpretations of these limits by using entangled states of the sensor system. One example is that of a spin-squeezed state, in which the uncertainty of one variable is decreased at the expense of another while still obeying Heisenberg's uncertainty principle, improving rotation sensitivity along a chosen axis. These states are potentially useful in devices including atomic clocks, inertial sensors, and magnetometers.</p>
<p>Any model of a quantum metrology device must respect the fact that physical measurements are not passive, as imagined classically, but necessarily invasive. Far from being a negative feature, well-understood quantum measurement can conditionally drive a system into desirable entangled states, including spin-squeezed states. Furthermore, the fundamental randomness of this process can, in principle, be removed with real-time feedback control, motivating an adaptation of classical feedback concepts to the quantum realm.</p>
<p>In this thesis, I describe these ideas in the context of one experimental example. A laser-cooled cloud of cesium spins is polarized along one axis via optical pumping and, subsequently, a linearly polarized far-off resonant probe beam traverses the sample. Due to the interaction Hamiltonian, the optical polarization rotates by an amount nominally proportional to one spin component of the collective spin state, enacting a weak, continuous, nondemolition measurement of that collective variable. This optical Faraday rotation is then measured with a polarimeter and the inherently noisy result used to condition the collective atomic state via a quantum filter, or stochastic master equation. Ideally, this process is capable of producing spin-squeezed states via the measurement itself.</p>
<p>The details of this measurement are investigated in depth, including a derivation of the nonideal polarizability Hamiltonian, an analysis of the projection process with control, and a derivation of the magnetometry sensitivity. Experimentally, we demonstrate continuous measurement of the collective spin state with a large single-shot signal-to-noise ratio and verify many predictions of the model. Finally, we describe attempts to observe the atomic projection noise, which would infer the preparation of spin-squeezed states.</p>https://resolver.caltech.edu/CaltechETD:etd-02172007-172548Dynamics and Simulation of Open Quantum Systems
https://resolver.caltech.edu/CaltechETD:etd-08072007-221313
Year: 2008
DOI: 10.7907/565E-JR05
<p>All systems are open to an essentially uncontrollable environment that acts as a source of decoherence and dissipation. In some cases the environment's only effect is to add a weak relaxation mechanism and thus can be ignored for short timescales. In others, however, the presence of the environment can fundamentally alter the behavior of the system. Such is the case in mesoscopic superconductors where the environment can stabilize superconductivity and in spin-boson systems where the environment induces a localization transition. Likewise, in technological applications we are often interested in systems operating far from equilibrium. Here the environment might act as a particle reservoir or strong driving force.</p>
<p>In all these examples, we need accurate methods to describe the influence of the environment on the system and to solve for the resulting dynamics or equilibrium states. In this thesis, we develop computational and conceptual approaches to efficiently simulate quantum systems in contact with an environment. Our starting point is the use of numerical renormalization techniques. Thus, we restrict our attention to one-dimensional lattices or small quantum systems coupled to an environment. We have developed several complementary algorithms: a superoperator renormalization algorithm for simulating real-time Markovian dynamics and for calculating states in thermal equilibrium; a blocking algorithm for simulating integro-differential equations with long-time memory; and a tensor network algorithm for branched lattices, which can be used to simulate strongly dissipative systems. Further, we provide support for an idea that to generically and accurately simulate the real-time dynamics of strongly dissipative systems, one has to include all or part of the environment within the simulation. In addition, we discuss applications and open questions.</p>https://resolver.caltech.edu/CaltechETD:etd-08072007-221313Coherent Control in Cavity QED
https://resolver.caltech.edu/CaltechETD:etd-05242008-114227
Year: 2008
DOI: 10.7907/RDB5-3862
<p>Advances in cavity quantum electrodynamics (QED) have allowed us to trap single cesium atoms within the field of a small optical resonator and to observe their strongly coupled interaction. However, in order to take advantage of this interaction as a resource for quantum information, we need to develop new techniques for control of the atom-cavity system. This thesis presents a series of experiments with the common goal of coherent control.</p>
<p>We have demonstrated the cooling of the center-of-mass motion of a trapped atom to its vibrational ground state along the cavity axis, and we have quantified the reversible nature of the process which maps a coherent state at the cavity input onto an atomic state. A new optical pumping method which exploits incoherent Raman transitions now allows us to prepare a trapped atom in any desired Zeeman state. I detail the technical steps which have enabled these results, including a conditional loading scheme which confirms the presence of at most one atom in the cavity. I outline our current efforts to characterize ground state population transfer via Raman transitions, which we hope will provide the basis for entanglement generation between atomic Zeeman states and photon polarization states. Two separate projects to construct new cavities and vacuum chamber systems are also discussed in the framework of future experiment design.</p>https://resolver.caltech.edu/CaltechETD:etd-05242008-114227Studies of Two Dimensional Electron Systems via Surface Acoustic Waves and Nuclear Magnetic Resonance Techniques
https://resolver.caltech.edu/CaltechETD:etd-11032007-160944
Year: 2008
DOI: 10.7907/E1X6-F676
<p>This thesis presents measurements investigating the spin degree of freedom in two dimensional electron systems (2DES’s). The measurements use nuclear magnetic resonance (NMR) techniques to study the role of spin in several 2DES states.</p>
<p>We first examine the spin transition that occurs in a half-filled Landau level in a single layer 2DES and compare our measurements to expectations from a composite fermion (CF) model. We show the temperature and density dependence of the nuclear T1 and resistively-detected NMR signal. The T₁ data can be roughly understood via a Korringa-like model of nuclear spin relaxation. However, the observed density dependence of both T₁ and the NMR signal is not explained by conventional CF theory.</p>
<p>We next consider a bilayer 2DES consisting of two closely spaced 2D electron layers, where each of the individual layers contains a half-filled Landau level. In this system, a transition occurs from a compressible single layer-like state to an incompressible correlated bilayer state as a function of the effective spacing between the two layers. When the effective spacing is made small enough, interactions between the two layers lead to the formation of a new state that can be viewed as a Bose condensate of excitons. Using NMR techniques we show that the spin degree of freedom is active during this transition.</p>
<p>In a single-layer 2DES with one completely filled Landau level (ν = 1), charged spin-texture excitations called skyrmions" are expected to exist. We probe the spin dynamics near this state using NMR. We find relatively fast nuclear relaxation rates that are consistent with a theory of spin excitations for a skyrmion solid. Our measurements also provide clues as to the origin of an "anomalous" NMR lineshape seen near ν=1.</p>
<p>We also present surface acoustic wave (SAW) measurements in a low density 2DES at zero magnetic field, under conditions where a 2D metal-insulator transition may occur. We find that our SAW data are consistent with a disorder-driven, percolation-type transition.</p>
https://resolver.caltech.edu/CaltechETD:etd-11032007-160944One-Dimensional Physics of Interacting Electrons and Phonons in Carbon Nanotubes
https://resolver.caltech.edu/CaltechETD:etd-10312008-123250
Year: 2009
DOI: 10.7907/RTMF-SF53
<p>The one-dimensional (1D) world is quite different from its higher dimensional counterparts. For example, the electronic ground state in 1D is not a Fermi liquid as in most solids, due to the role of electron-electron interactions. Most commonly, electrons in 1D are described as a <i>Luttinger liquid</i>, where the low-energy excitations are decoupled bosonic charge and spin waves. Carbon nanotubes are clean 1D systems which have been shown to behave like a Luttinger liquid at high electron density. However, at low electron density and in the absence of disorder, the ground state is predicted to be a <i>1D Wigner crystal</i>—an electron solid dominated by long-range Coulomb interaction. Moreover, short-range interaction mediated by the atomic lattice (umklapp scattering) is predicted to transform a nominal 1D metal into a <i>Mott insulator</i>.</p>
<p>In this thesis, we develop techniques to make extremely clean nanotube single-electron transistors. We study them in the few-electron/hole regime using Coulomb blockade spectroscopy in a magnetic field. In semiconducting nanotubes, we map out the antiferromagnetic exchange coupling as a function of carrier number and find excellent agreement to a Wigner crystal model. In nominally metallic nanotubes, we observe a universal energy gap in addition to the single-particle bandgap, implying that nanotubes are never metallic. The magnitude, radius dependence and low-energy neutral excitations of this additional gap indicate a Mott insulating origin.</p>
<p>Further, we use simultaneous electrical and Raman spectroscopy measurements to study the phonons scattered by an electric current. At high bias, suspended nanotubes show striking negative differential conductance, attributed to non-equilibrium phonons. We directly observe such "hot" phonon populations in the Raman response and also report preferential electron coupling to one of two optical phonon modes. In addition, using spatially-resolved Raman spectroscopy, we obtain a wealth of local information including the 1D temperature profile, a spatial map of the thermal conductivity and thermal contact resistances, which reveal the mechanism of thermal transport in nanotubes.</p>
<p>Finally, with multi-wall nanotubes (MWNTs), we use electrical breakdown as thermometry to provide evidence for ballistic phonon propagation and obtain an estimate for the quantum of thermal conductance. We also develop linear-bearing nanoswitches using the low-friction properties of MWNTs.</p>
https://resolver.caltech.edu/CaltechETD:etd-10312008-123250Non-Abelian Quantum Hall States and Fractional Statistics
https://resolver.caltech.edu/CaltechETD:etd-05122009-142703
Year: 2009
DOI: 10.7907/WQC4-W268
The discovery of the fractional quantum Hall effect stimulated the investigation of anyons, particles with fractional statistics which are neither bosons nor fermions. This thesis focuses on the study of quantum Hall states which may support non-Abelian anyons. We first address the validity of assumptions used in the numerical study of such states, and then proceed with analyzing different experiments which can detect non-Abelian fractional statistics. We quantitatively analyze the two-point contact interferometer experiment, which is hoped to display clear-cut, direct evidence of non-Abelian fractional statistics. We calculate the temperature and voltage dependence of the interference experiment outcome, and the signal attenuation due to finite temperature loss of coherence. We then analyze the edge theory of a family of non-Abelian quantum Hall states in the second Landau level, and examine the tunneling between these states and a quantum dot. This tunneling problem maps onto the multi-channel Kondo problem, and will allow distinguishing between different quantum Hall states. Finally, we use the same theoretical methods for analyzing Sagnac interference in the conductance of a carbon nanotube loop, a one-dimensional system.
https://resolver.caltech.edu/CaltechETD:etd-05122009-142703Stochastic and Collective Properties of Nonlinear Oscillators
https://resolver.caltech.edu/CaltechETD:etd-06012009-145134
Year: 2009
DOI: 10.7907/93R8-TJ70
<p>Two systems of nonlinear oscillators are considered: (a) a single periodically driven nonlinear oscillator interacting with a heat bath, which may operate in the regime of bistability or monostability, and (b) a one-dimensional chain of self-sustaining phase oscillators with nearest-neighbor interaction.</p>
<p>For a single oscillator we analyze the scaling crossovers in the thermal activation barrier between the two stable states. The rate of metastable decay in nonequilibrium systems is expected to display scaling behavior: the logarithm of the decay rate should scale as a power of the distance to a bifurcation point where the metastable state disappears. We establish the range where different scaling behavior is displayed and show how the crossover between different types of scaling occurs. Using the instanton method, we map numerically the entire parameter range of bistability and find the regions where the scaling exponents are 1 or 3/2, depending on the damping. The exponent 3/2 is found to extend much further from the bifurcation then where it would be expected to hold as a result of an overdamped soft mode. Additionally, we uncover a new scaling behavior with exponent of ≈1.3 that extends beyond the close vicinity of the bifurcation point.</p>
<p>We also study the pattern of fluctuational trajectories in the monostable regime. For nonequilibrium systems, fluctuational and relaxational trajectories are not simply related by time-reversibility, as is the case in thermal equilibrium. One of the consequences of this is the onset of singularities in the pattern of fluctuational trajectories, where most probable paths to neighboring states are far away from each other. This also creates nonsmoothness in the probability distribution of the system in its phase space. We discover that the pattern of optimal paths in equilibrium systems is fragile with respect to the driving strength F, and investigate how the singularities occur as the system is driven away from equilibrium. As the strength of the driving F approaches zero, the cusp of the spiral caustic system recedes to larger radius R and the angle of the cusp also decreases. The dependence of R on F displays two scaling laws with crossovers, where the scaling exponents depend on the damping.</p>
<p>For the one-dimensional chain of nearest-neighbor coupled phase oscillators, we develop a renormalization group method to investigate synchronization clusters. We apply it numerically to Lorentzian distributions of intrinsic frequencies and couplings and investigate the statistics of the resultant cluster sizes and frequencies. We find that the distributions of sizes of frequency clusters are exponential, with a characteristic length. The dependence of this length upon parameters of these Lorentzian distributions develops an asymptotic power law with an exponent of 0.48 ± 0.02. The findings obtained with the renormalization group are compared with numerical simulations of the equations of motion of the chain, with an excellent agreement in all the aforementioned quantities.</p>
https://resolver.caltech.edu/CaltechETD:etd-06012009-145134Thermal Properties and Nanoelectromechanical System Based on Carbon Nanotubes
https://resolver.caltech.edu/CaltechETD:etd-03272009-033303
Year: 2009
DOI: 10.7907/2T53-P806
<p>In Chapter I, the fundamental electronic properties of two-dimensional (2D) graphene and one-dimensional (1D) carbon nanotubes are discussed, along with the carbon nanotube single-electron transistors (SETs). In addition to nanotubes' extraordinary electronic properties, the phenomena of phonon transport in carbon nanotubes are also notable. In Chapter II, we discuss our experiments probing the thermal properties of multi-walled carbon nanotubes. We exploit the specific breakdown temperature under a large current, which provides an effective thermometer, in conjunction with the known power input to measure the thermal conductivity of the nanotubes. Our results reveal the exceptional micron-scale phonon mean free path at temperatures approaching 900K, and we demonstrate the first evidence for ballistic phonon propagation in nanotubes, reaching a regime where the thermal conductance of nanotubes is limited only by fundamental quantum mechanical limits imposed by their 1D nature.</p>
<p>Moreover, the combination of remarkable electrical and mechanical properties makes carbon nanotubes a highly promising candidate for nanoelectromechanical systems (NEMS). In Chapter III, we investigate using doubly clamped suspended single-walled carbon nanotubes as nanomechanical resonators at cryogenic temperatures. Their intrinsic single-electron transistor behavior provides a mixing mechanism to self-detect their motion based on their capacitance to a nearby gate electrode. We exploit our devices to attain an ultrasensitive mass sensor, realizing atomic-scale mass sensing. Finally, in Chapter IV, nanoelectromechanical switches based on using multi-walled carbon nanotubes as nanoscale linear bearings are discussed. First we demonstrate the preparation of the initial OFF state by using electrical breakdown to create gaps in a free-standing MWNT device, while subsequently the ON state is actuated with electrical forces and undergoes linear bearing motion that telescopes the inner shells to bridge the gaps. The switching cycle can be performed in double-walled nanotube devices by restoring the insulating OFF state with a controllable gate voltage. These tubular switches can potentially serve as nonvolatile memory or logic gate elements.</p>
https://resolver.caltech.edu/CaltechETD:etd-03272009-033303Characterization and Control of a Strongly-Coupled Atom-Cavity System
https://resolver.caltech.edu/CaltechETD:etd-05152009-142724
Year: 2009
DOI: 10.7907/HZB5-MM65
<p>In recent years, remarkable advances in the science of laser cooling and trapping of atomic samples have lead to breakthroughs in quantum optics and, in particular, in cavity quantum electrodynamics (QED). The ability to optically trap an atom within the mode of a ultra-high finesse cavity of small mode volume for experimentally significant periods of time now allows for the continuous observation of fundamental quantum optical effects. This dissertation will focus on experiments conducted to fully characterize and exert quantum control over a strongly-coupled atom-cavity system consisting of single cesium atoms isolated by a dipole trapping in the mode of a Fabry-Perot optical resonator.</p>
<p>In particular, we describe techniques developed and implemented for exerting coherent control over the internal and quantum motional state of these atoms using stimulated Raman processes. We also focus on the applications of this system to quantum networking and quantum information science, particularly within the context of coherently transferring quantum states from atom to quantum optical fields and back. Finally, we describe a series of measurements carried out to explore the characteristic dynamics of the Jaynes-Cummings Hamiltonian which governs the system. This includes spectroscopic measurement of the signature vacuum Rabi splitting for strongly-coupled cavity QED as well as evidence in the time domain for coherent Rabi nutation of excitation between atom and field on resonance.</p>
https://resolver.caltech.edu/CaltechETD:etd-05152009-142724Investigations of Nanoscale Variations in Spin and Charge Transport in Manganites and Organic Semiconductors Using Spin Polarized Scanning Tunneling Spectroscopy
https://resolver.caltech.edu/CaltechTHESIS:02082010-153048901
Year: 2010
DOI: 10.7907/TX09-6W39
<p>Spintronics is a new class of spin-dependent electronics with great potential for nonvolatile memory and logic technology. Additionally, spintronics may be combined with optoelectronic applications to achieve higher efficiency and novel capabilities. All of these developments require growth and characterization of new materials to polarize and transport electron spin currents. In this context, spin-polarized and non spin-polarized spatially resolved conductance measurements performed by scanning tunneling microscopy (STM) are effective means to investigate the spin and charge quantum transport in magnetic and organic systems, particularly for systems that are prone to phase separations and complex magnetic properties, such as the colossal magnetoresistive (CMR) manganites La<sub>1-x</sub>Ca<sub>x</sub>MnO<sub>3</sub> (LCMO) that are known to exhibit intrinsic electronic heterogeneity due to strong electronic correlation and competing orders in the ground state. Additionally, STM measurements can provide direct information about the band structure and mobility of the organic semiconductor 8-hydroxyquinoline aluminum (Alq<sub>3</sub>) in the Alq<sub>3</sub>/LCMO heterostructures to further understand their performance in spintronic devices.</p>
<p>The manganite compound La<sub>1-x</sub>Ca<sub>x</sub>MnO<sub>3</sub> (LCMO) with a bulk doping level x = 0.3 is a ferromagnetic metal with a relatively high Curie temperature T<sub>c</sub> = 270K. This system is promising for spintronic device applications, and may be used as a spin current injector because of the gapped band structure for minority spins, a property known as half-metallicity. On the other hand, even in this bulk ferromagnetic metallic phase, inherent electronic inhomogeneity at microscopic scales is expected. To further study this effect, we have investigated x = 0.3 LCMO thin films using scanning tunneling microscopy in spectroscopic mode under varied temperature, magnetic field and spin polarization of the tunneling current. Spatially resolved maps of tunneling conductance taken with non polarized Pt/Ir tip show variations on the scale of a few hundred nanometers in size in the bulk ferromagnetic state, which are believed to be the result of intrinsic inhomogeneity of the manganites due to their tendency toward phase separation. Maps of tunneling conductance taken with spin-polarized Cr coated tips are consistent with the convolution of the LCMO and Cr density of states, and below the T<sub>c</sub> of LCMO the spin-polarized tunnel junction can be described as a spin valve configuration. The electronic homogeneity in the material increases above the magnetic ordering temperature, or with application of magnetic field in the bulk ferromagnetic state. We identified gaps in the conductance at two separate characteristic energies. The first gap of energy approximately 0.6 eV is believed to arise from a ferromagnetic insulator (FI) surface phase due to its disappearance above the Curie temperature (T<sub>c</sub>) and the dependence of gap energy on relative tip and sample magnetic orientation. The surface phase may be stabilized by Ca deficiency at the LCMO surface, corroborated by x-ray photoemission spectroscopy (XPS). Second, we observe a nearly temperature independent and spatially varying gap of approximately 0.4 eV for all zero-field tunneling spectra, which is believed to be associated with the psuedogap (PG) phenomena in the manganites. Application of a magnetic field converts the regions of PG phenomena to FI, in conjunction with an increase in the homogeneity of the lm conductance. These findings suggest that the PG phenomena arise from electronic inhomogeneity in the manganite film, in agreement with theoretical investigations, and that the vertical and lateral electronic inhomogeneity, along with its dependence on temperature and applied magnetic field, has important implications for use of these materials in high-density nanoscale spintronic devices.</p>
<p>We have also successfully deposited and investigated Alq<sub>3</sub>/LCMO heterostructures of varying thicknesses to investigate charge transport in Alq<sub>3</sub>. Bulk Alq<sub>3</sub> structural properties are preserved down to 10 nm in thickness with a -0.3 eV offset in band energies. The lack of band bending between LCMO and Alq<sub>3</sub> is suggestive of a shift in the preferred isomer from meridinial to facial at the interface. The absence of polaron states from our STM studies implies the relative unimportance of polarons in Alq<sub>3</sub> for this heterostructure. In addition, the measured mobilities on the order of 10<sup>-5</sup>cm<sup>2</sup>(Vs)<sup>-1</sup> for electrons and holes in Alq<sub>3</sub> lms deposited on heated LCMO substrates more closely resemble values of the intrinsic mobility estimated from the muon spin relaxation measurements than those from studies of the bulk LED structures, suggesting that superior film conductivity close to the fundamental limit is possible with a heated substrate during sublimation.</p>
https://resolver.caltech.edu/CaltechTHESIS:02082010-153048901Variational Studies of Exotic Bose Liquid, Spin Liquid, and Magnetic Phases
https://resolver.caltech.edu/CaltechTHESIS:05282011-122022010
Year: 2011
DOI: 10.7907/1QT1-PN18
The strong interest in strongly correlated systems in condensed matter physics has continued unabated for the past few decades. In recent years, the number of novel, exotic quantum phases found in theoretical studies has seen a phenomenal rise. Among those interesting quantum states are bose liquids and spin liquids, where strong quantum fluctuations have prevented the systems from developing a long range order. Our work in this thesis seeks to further the understanding of frustrated systems. In the study of a hard-core boson model with ring-only exchange interactions on a square lattice, we obtain concrete numerical realization of the unconventional Exciton Bose Liquid (EBL) phase, which possesses interesting properties such as a "Bose surface" which resembles the Fermi surface in a metal, as well as unusual thermodynamic properties such as a T Log T dependence for specific heat. An equally important result from this work is the demonstration that the widely used Gutzwiller projection on slave-particle wave functions may generally fail to capture the correct long wavelength physics in the respective systems. For the Heisenberg antiferromagnet on the kagome lattice, which is a promising candidate for realizing a spin-disordered ground state, our variational study shows that the projected Schwinger boson wave function is energetically better than the Dirac spin liquid wave function when a small antiferromagnetic second-neighbor spin coupling is added to the nearest-neighbor model. We also study the anisotropic triangular Heisenberg antiferromagnetic in magnetic field, and find simple, yet accurate wave functions for various regions of the surprisingly rich phase diagram, thus providing insights into the energetics of the competing phases in this interesting model. Finally, our work also highlights permanent-type wave functions as potentially useful constructions in variational studies of systems with short-ranged correlations, e.g., a Mott insulator and a gapped spin liquid.https://resolver.caltech.edu/CaltechTHESIS:05282011-122022010Case Studies in Quantitative Biology: Biochemistry on a Leash and a Single-Molecule Hershey-Chase Experiment
https://resolver.caltech.edu/CaltechTHESIS:05112011-144451576
Year: 2011
DOI: 10.7907/FJW3-G615
<p>The last 50 years of biological research has seen a marked increase in the amount of quantitative data that describes living systems. This wealth of data provides a unique opportunity to recast the pictorial level descriptions of biological processes in the language of mathematics, with the hope that such an undertaking will lead to deeper insights into the behavior of living systems. To achieve this end, we have undertaken three case studies in physical biology. In the first case study, we used statistical mechanics and polymer physics to construct a simple model that describes how flexible chains of amino acids, referred to as tethers, influence the information processing properties of signaling proteins. In the second case study, we studied the DNA ejection process of phage lambda <i>in vitro</i>. In particular, we used bulk and single-molecule methods to study the control parameters that govern the force and kinematics of the ejection process <i>in vitro</i>. In the last case study, we studied the DNA ejection process of phage lambda <i>in vivo</i>. We developed an assay that allows real-time monitoring of DNA ejection <i>in vivo</i> at the single-molecule level. We also developed a parallel system that allows the simultaneous visualization of both phage capsids and phage DNA at the single-cell level, constituting a true single-molecule Hershey-Chase experiment. The work described in this thesis outlines new tools, both in theory and experiment, that can be used to study biological systems as well as a paradigm that can be employed to mathematicize the cartoons of biology.</p>https://resolver.caltech.edu/CaltechTHESIS:05112011-144451576Simulation of Strongly Correlated Quantum Many-Body Systems
https://resolver.caltech.edu/CaltechTHESIS:04082011-161930834
Year: 2011
DOI: 10.7907/FQDK-A221
In this thesis, we address the problem of solving for the properties of interacting quantum many-body systems in thermal equilibrium. The complexity of this problem increases exponentially with system size, limiting exact numerical simulations to very small systems. To tackle more complex systems, one needs to use heuristic algorithms that approximate solutions to these systems. Belief propagation is one such algorithm that we discuss in chapters 2 and 3. Using belief propagation, we demonstrate that it is possible to solve for static properties of highly correlated quantum many-body systems for certain geometries at all temperatures. In chapter 4, we generalize the multiscale renormalization ansatz to the anyonic setting to solve for the ground state properties of anyonic quantum many-body systems. The algorithms we present in chapters 2, 3, and 4 are very successful in certain settings, but they are not applicable to the most general quantum mechanical systems. For this, we propose using quantum computers as we discuss in chapter 5. The dimension reduction algorithm we consider in chapter 5 enables us to prepare thermal states of any quantum many-body system on a quantum computer faster than any previously known algorithm. Using these thermal states as the initialization of a quantum computer, one can study both static and dynamic properties of quantum systems without any memory overhead.https://resolver.caltech.edu/CaltechTHESIS:04082011-161930834Quantum Phases and Phase Transitions in Disordered Low-Dimensional Systems: Thin Film Superconductors, Bilayer Two-Dimensional Electron Systems, and One-Dimensional Optical Lattices
https://resolver.caltech.edu/CaltechTHESIS:09082010-155113346
Year: 2011
DOI: 10.7907/M4BX-7511
The study of various quantum phases and the phase transitions between them in low-dimensional disordered systems has been a central theme of recent developments of condensed matter physics. Examples include disordered thin film superconductors, whose critical temperature and density of states can be affected by a normal metallic layer deposited on top of them; amorphous thin films exhibiting superconductor-insulator transitions (SIT) tuned by disorder or magnetic field; and bilayer two-dimensional electron systems at total filling factor ν=1, which exhibit interlayer coherent quantum Hall state at small layer separation and have a phase transition tuned by layer separation, parallel magnetic field, density imbalance, or temperature. Although a lot of theoretical and experimental investigations have been done, many properties of these phases and natures of the phase transitions in these systems are still being debated. Here in this thesis, we report our progress towards a better understanding of these systems. For disordered thin film superconductors, we first propose that the experimentally observed lower-than-theory gap-T<sub>c</sub> ratio in bilayer superconducting-normal-metal films is due to inhomogeneous couplings. Next, for films demonstrating superconductor-insulator transitions, we propose a new type of experiment, namely the drag resistance measurement, as a method capable of pointing to the correct theory among major candidates such as the quantum vortex picture and the percolation picture. For bilayer two-dimensional electron systems, we propose that a first-order phase transition scenario and the resulting Clausius-Clapeyron equations can describe various transitions observed in experiments quite well. Finally, in one-dimensional optical lattices, we show that one can engineer the long-sought-after random hopping model with only off-diagonal disorder by fast-modulating an Anderson insulator.https://resolver.caltech.edu/CaltechTHESIS:09082010-155113346Coherent Control of Entanglement with Atomic Ensembles
https://resolver.caltech.edu/CaltechTHESIS:05192011-130117986
Year: 2011
DOI: 10.7907/9T7P-2C53
<p>Quantum networks are composed of quantum nodes which coherently interact by way of quantum channels. They offer powerful capabilities for quantum computation, communication, and metrology. A generic requirement for these realizations is the capability to generate and store quantum states among multiple quantum nodes, and to disseminate these resources throughout the network via the quantum channels. In this thesis, I describe a series of experiments whereby single excitations in atomic ensembles are strongly coupled to optical modes and provide efficient means for the coherent control of entangled states between matter and light.</p>
<p>By following the seminal proposal by Duan et al., we have generated measurement-induced entanglement of an excitation between two cold atomic ensembles. Using this system, we investigated the relationship for the global bipartite entanglement and local correlations in its subsystems.</p>
<p>In addition, we achieved functional quantum nodes for entanglement distribution. Two pairs of remote ensembles at two quantum nodes were prepared into entangled states in a heralded and asynchronous fashion by the conditional controls of the entanglement. The quantum states of the ensembles were then distributed into polarization entangled states of photons. We also prepared an analogous quantum state and transferred the nonlocal coherence between two pairs of heralded entangled atomic ensembles, providing a step towards entanglement connection.</p>
<p>Beyond such probabilistic approaches, we demonstrated an experiment where entanglement between two quantum memories is created by the reversible and deterministic mapping of an entangled state of light via dynamic electromagnetically induced transparency. This experiment opens novel prospects of integrating hybrid quantum systems by way of reversible quantum interfaces between light and matter.</p>
<p>Then, we extended our work to multipartite quantum systems. We theoretically investigated the characterization of multipartite mode-entangled states by way of quantum uncertainty relations, and introduced theoretical tools to verify the entanglement orders in multipartite systems. In particular, we achieved entanglement for one delocalized photon among multiple optical modes (N > 2).</p>
<p>Finally, we have achieved measurement-induced entanglement of spin waves among four quantum memories. The individual atomic components for the entangled W state of the four ensembles were then coherently converted into four propagating entangled beams of light via superradiant emissions. We observed the statistical and dynamic transitions for the multipartite entangled spin waves. Experiments described in this thesis thereby represent significant advances of experimental and theoretical capabilities to generate, store, transfer, and characterize entanglement of matter and light over quantum networks.</p>https://resolver.caltech.edu/CaltechTHESIS:05192011-130117986Emerging Paradigms in Quantum Error Correction and Quantum Cryptography
https://resolver.caltech.edu/CaltechTHESIS:05312011-104108847
Year: 2011
DOI: 10.7907/T8HP-7R18
<p>We study two novel paradigms in quantum error correction and quantum cryptography — approximate quantum error correction and noisy-storage cryptography — which explore alternate approaches for dealing with quantum noise. Approximate quantum error correction seeks to relax the constraint of perfect error correction and construct codes that might be better adapted to correct for specific noise models. Noisy-storage cryptography relies on the power of quantum noise to execute two-party cryptographic tasks securely.</p>
<p>Motivated by examples of approximately correcting codes, which make use of fewer physical resources than perfect codes and still obtain comparable levels of fidelity, we study the problem of finding and characterizing such codes in general. We construct for the first time a universal, near-optimal recovery map for approximate quantum error correction (AQEC), with optimality defined in terms of worst-case fidelity. Using the analytical form of this recovery, we also obtain easily verifiable conditions for AQEC. This in turn leads to a simple algorithm for identifying good approximate codes, without having to perform a difficult optimization over all recovery maps for every possible encoding.</p>
<p>Noisy-storage cryptography envisions a setting where two-party cryptographic protocols can be securely implemented based solely on the assumption that the quantum storage device possessed by either party is noisy and bounded. Here, we construct two-party protocols (using higher-dimensional states) that are secure even when a dishonest player can store all but a small fraction of the information transmitted during the protocol, in his noiseless quantum memory. We also show that when his memory is noisy, security can be extended to a larger class of noisy quantum memories. Our result demonstrates that the physical limits of the quantum noisy-storage model are indeed achievable, albeit asymptotically.</p>
<p>We also describe our investigations on obtaining strong entropic uncertainty relations using symmetric complementary bases. Uncertainty relations are an important and useful resource in analyzing the security of quantum cryptographic protocols, in addition to being of interest from a foundational standpoint. We present a novel construction of sets of symmetric, complementary bases in dimension d = 2<sup>n</sup>, which are cyclically permuted under the action of a unitary transformation. We also obtain new lower bounds for uncertainty relations in terms of the min-entropy, which are tight for specific instances of our construction.</p>https://resolver.caltech.edu/CaltechTHESIS:05312011-104108847Ladder Studies of Gapless Quantum Spin Liquids: Spin Bose-metal and SU(2)-invariant Majorana Spin Liquids
https://resolver.caltech.edu/CaltechTHESIS:05142012-220503327
Year: 2012
DOI: 10.7907/YDSP-0M98
<p>The recent experimental realizations of spin-1/2 gapless quantum spin liquids in two-dimensional triangular lattice organic compounds EtMe<sub>3</sub>Sb[Pd(dmit)<sub>2</sub>]<sub>2</sub> and κ-(ET)<sub>2</sub>Cu<sub>2</sub>(CN)<sub>3</sub> 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.</p>
https://resolver.caltech.edu/CaltechTHESIS:05142012-220503327Quantum Nonequilibrium Physics with Rydberg Atoms
https://resolver.caltech.edu/CaltechTHESIS:05232012-231713032
Year: 2012
DOI: 10.7907/0N4R-5Y37
<p>A Rydberg atom is an atom excited to a high energy level, and there is a strong dipole-dipole interaction between nearby Rydberg atoms. While there has been much interest in closed systems of Rydberg atoms, less is known about open systems of Rydberg atoms with spontaneous emission. This thesis explores the latter.</p>
<p>We consider a lattice of atoms, laser-excited from the ground state to a Rydberg state and spontaneously decaying back to the ground state. Using mean-field theory, we study the how the steady-state Rydberg population varies across the lattice. There are three phases: uniform, antiferromagnetic, and oscillatory.</p>
<p>Then we consider the dynamics of the quantum model when mean-field theory predicts bistability. Over time, the system occasionally jumps between a state of low Rydberg population and a state of high Rydberg population. We explain how entanglement and quantum measurement enable the jumps, which are otherwise classically forbidden.</p>
<p>Finally, we let each atom be laser-excited to a short-lived excited state in addition to a Rydberg state. This three-level configuration leads to rich spatiotemporal dynamics that are visible in the fluorescence from the short-lived excited state. The atoms develop strong spatial correlations that change on a long time scale.</p>https://resolver.caltech.edu/CaltechTHESIS:05232012-231713032Studies of Exciton Condensation and Transport in Quantum Hall Bilayers
https://resolver.caltech.edu/CaltechTHESIS:09262011-144749993
Year: 2012
DOI: 10.7907/PQJV-SB92
This thesis is a report of the transport properties of bilayer two-dimensional electron systems found in GaAs/AlGaAs double quantum well semiconductor heterostructures. When a strong perpendicular magnetic field is applied so that the total Landau filling factor is equal to one and if the two layers are close enough together, a novel quantum Hall (QH) state with strong interlayer correlations can form. This QH state is often described as an excitonic condensate, in which electrons in one layer pair with holes in the other. As neutral particles, excitons feel no Lorentz force and are not confined to the edges of the bilayer system like charged quasiparticles are. Instead, excitons are expected to be able to move freely through the bulk and even flow without any dissipation under proper conditions (i.e.,~excitonic superfluidity). Counterflow studies that directly probe the bulk verify this exciton transport in the electrically insulating interior. We also report on studies of the phase boundary between the correlated and uncorrelated phases at total Landau filling factor one as the effective interlayer separation is tuned. When both phases are fully spin polarized at high Zeeman energy, the phase transition is much broader than when the uncorrelated phase is incompletely polarized at low Zeeman energy. This suggests a possible change in the nature of the phase transition in the regime of complete spin polarization.https://resolver.caltech.edu/CaltechTHESIS:09262011-144749993Conditional Independence in Quantum Many-Body Systems
https://resolver.caltech.edu/CaltechTHESIS:05102013-172241867
Year: 2013
DOI: 10.7907/PZJN-A841
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.https://resolver.caltech.edu/CaltechTHESIS:05102013-172241867The Interplay of Localization and Interactions in Quantum Many-Body Systems
https://resolver.caltech.edu/CaltechTHESIS:05292013-170142035
Year: 2013
DOI: 10.7907/37K7-6Q13
<p>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.</p>
<p>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.</p>
<p>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.</p>
https://resolver.caltech.edu/CaltechTHESIS:05292013-170142035Lattice Quantum Codes and Exotic Topological Phases of Matter
https://resolver.caltech.edu/CaltechTHESIS:05292013-140541902
Year: 2013
DOI: 10.7907/GCYW-ZE58
<p>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.</p>
<p>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.</p>
<p>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.</p>https://resolver.caltech.edu/CaltechTHESIS:05292013-140541902Nonlinear Optics and Wavelength Translation Via Cavity-Optomechanics
https://resolver.caltech.edu/CaltechTHESIS:05312013-144103500
Year: 2013
DOI: 10.7907/DKW6-TF64
<p>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.</p>
<p>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.</p>
<p>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.</p>
<p>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.</p>https://resolver.caltech.edu/CaltechTHESIS:05312013-144103500The Combinatorics of Transcriptional Regulation
https://resolver.caltech.edu/CaltechTHESIS:05162014-140751409
Year: 2014
DOI: 10.7907/PNX5-Y638
The ability to regulate gene expression is of central importance for the adaptability of living organisms to changes in their internal and external environment. At the transcriptional level, binding of transcription factors (TFs) in the vicinity of promoters can modulate the rate at which transcripts are produced, and as such play an important role in gene regulation. TFs with regulatory action at multiple promoters is the rule rather than the exception, with examples ranging from TFs like the cAMP receptor protein (CRP) in <i>E. coli</i> that regulates hundreds of different genes, to situations involving multiple copies of the same gene, such as on plasmids, or viral DNA. When the number of TFs heavily exceeds the number of binding sites, TF binding to each promoter can be regarded as independent. However, when the number of TF molecules is comparable to the number of binding sites, TF titration will result in coupling ("entanglement") between transcription of different genes. The last few decades have seen rapid advances in our ability to quantitatively measure such effects, which calls for biophysical models to explain these data. Here we develop a statistical mechanical model which takes the TF titration effect into account and use it to predict both the level of gene expression and the resulting correlation in transcription rates for a general set of promoters. To test these predictions experimentally, we create genetic constructs with known TF copy number, binding site affinities, and gene copy number; hence avoiding the need to use free fit parameters. Our results clearly prove the TF titration effect and that the statistical mechanical model can accurately predict the fold change in gene expression for the studied cases. We also generalize these experimental efforts to cover systems with multiple different genes, using the method of mRNA fluorescence in situ hybridization (FISH). Interestingly, we can use the TF titration affect as a tool to measure the plasmid copy number at different points in the cell cycle, as well as the plasmid copy number variance. Finally, we investigate the strategies of transcriptional regulation used in a real organism by analyzing the thousands of known regulatory interactions in <i>E. coli</i>. We introduce a "random promoter architecture model" to identify overrepresented regulatory strategies, such as TF pairs which coregulate the same genes more frequently than would be expected by chance, indicating a related biological function. Furthermore, we investigate whether promoter architecture has a systematic effect on gene expression by linking the regulatory data of <i>E. coli</i> to genome-wide expression censuses.https://resolver.caltech.edu/CaltechTHESIS:05162014-140751409Electronic States in Disordered Topological Insulators
https://resolver.caltech.edu/CaltechTHESIS:06022014-093929164
Year: 2014
DOI: 10.7907/BSH1-AA62
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<sub>2</sub>Se<sub>3</sub> and Bi<sub>2</sub>Te<sub>3</sub> 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.https://resolver.caltech.edu/CaltechTHESIS:06022014-093929164Light-Matter Interactions in Semiconductors and Metals: From Nitride Optoelectronics to Quantum Plasmonics
https://resolver.caltech.edu/CaltechTHESIS:06052015-164458210
Year: 2015
DOI: 10.7907/Z9513W4S
<p>This thesis puts forth a theory-directed approach coupled with spectroscopy aimed at the discovery and understanding of light-matter interactions in semiconductors and metals.</p>
<p>The first part of the thesis presents the discovery and development of Zn-IV nitride materials.The commercial prominence in the optoelectronics industry of tunable semiconductor alloy materials based on nitride semiconductor devices, specifically InGaN, motivates the search for earth-abundant alternatives for use in efficient, high-quality optoelectronic devices. II-IV-N2 compounds, which are closely related to the wurtzite-structured III-N semiconductors, have similar electronic and optical properties to InGaN namely direct band gaps, high quantum efficiencies and large optical absorption coefficients. The choice of different group II and group IV elements provides chemical diversity that can be exploited to tune the structural and electronic properties through the series of alloys. The first theoretical and experimental investigation of the ZnSnxGe1−xN2 series as a replacement for III-nitrides is discussed here.</p>
<p>The second half of the thesis shows ab−initio calculations for surface plasmons and plasmonic hot carrier dynamics. Surface plasmons, electromagnetic modes confined to the surface of a conductor-dielectric interface, have sparked renewed interest because of their quantum nature and their broad range of applications. The decay of surface plasmons is usually a detriment in the field of plasmonics, but the possibility to capture the energy normally lost to heat would open new opportunities in photon sensors, energy conversion devices and switching. A theoretical understanding of plasmon-driven hot carrier generation and relaxation dynamics in the ultrafast regime is presented here. Additionally calculations for plasmon-mediated upconversion as well as an energy-dependent transport model for these non-equilibrium carriers are shown.</p>
<p>Finally, this thesis gives an outlook on the potential of non-equilibrium phenomena in metals and semiconductors for future light-based technologies.</p>https://resolver.caltech.edu/CaltechTHESIS:06052015-164458210Disorder Driven Transitions in Non-Equilibrium Quantum Systems
https://resolver.caltech.edu/CaltechTHESIS:05262016-092645359
Year: 2016
DOI: 10.7907/Z9MK69VV
<p>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 <i>all</i> the eigenstates of the Hamiltonian are studied, as a function of the power-law exponent of the hopping amplitude. </p>
<p>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. </p>
<p>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.</p>
<p>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.</p>
<p>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.</p>https://resolver.caltech.edu/CaltechTHESIS:05262016-092645359Toward Realizable Quantum Computers
https://resolver.caltech.edu/CaltechTHESIS:06072016-162802972
Year: 2016
DOI: 10.7907/Z96M34SC
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. https://resolver.caltech.edu/CaltechTHESIS:06072016-162802972Nonlinear and Ultrafast Optical Investigations of Correlated Materials
https://resolver.caltech.edu/CaltechTHESIS:06092017-141136995
Year: 2017
DOI: 10.7907/Z9VD6WHV
<p>This thesis comprises studies of 3<i>d</i>-5<i>d</i> 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<sub>2</sub>RuO<sub>4</sub> and Sr<sub>2</sub>IrO<sub>4</sub>, discovered novel electronic phases in doped Sr<sub>2</sub>IrO<sub>4</sub> and Sr<sub>3</sub>Ir<sub>2</sub>O<sub>7</sub>, and investigated different types of antiferromagnetic orders in transition metal trichalcogenides MPX<sub>3</sub>.</p>
https://resolver.caltech.edu/CaltechTHESIS:06092017-141136995Thermalization in Periodically-Driven Interacting Quantum Systems
https://resolver.caltech.edu/CaltechTHESIS:06062018-171256773
Year: 2018
DOI: 10.7907/3G0V-TW52
<p>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 <i>engineering</i> 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.</p>
<p>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.</p>https://resolver.caltech.edu/CaltechTHESIS:06062018-1712567732D and 3D Photonic Crystals: Synthesis, Characterization and Topological Phenomenon
https://resolver.caltech.edu/CaltechTHESIS:09112017-095117655
Year: 2018
DOI: 10.7907/Z9NZ85V2
<p>Topological photonics has become an increasingly popular research topic in the field of nanophotonics in recent years. Topological phases of light provide opportunities to manipulate light propagation efficiently at the nanoscale volume. Performance of conventional optical elements are limited by back-reflection and bending losses, which hinder their prospect of large scale integration. Topological protection enables unidirectional excitation of edge states or surface states without leaking into the bulk, as well as suppression of scattering when encountering defects and corners. With such advantages, topological photonic elements may surpass conventional photonic
design for future generations of ultra-compact efficient computing, imaging, and sensing applications. Due to limitations of fabrication and characterization techniques, previously experimental efforts on topological photonics have been carried out with 2D micron-scale optical design or at the microwave wavelength.</p>
<p>This thesis contributes to the experimental development of topological photonics in two aspects: first, how to fabricate and characterize 3D photonic crystals and therefore extend topological protection into the 3D (Chapters 2-3); and second, how to realize nanoscale topological protection in the visible frequencies (chapters 4-6). Specifically, Chapter 2 reports fabrication of 3D single gyroid structures composed of a-Si and FTIR characterization of a photonic bandgap at the mid-infrared wavelength. This is the foundation to investigate more complex morphologies to introduce topologically nontrivial photonic states. Chapter 3 describe properties of
double gyroid photonic crystals, followed by angle resolved characterization method in the mid-infrared. Double gyroid photonic crystals can be designed to possess quadratic degeneracy points, Weyl points, and line nodes. Since Weyl points have non-zero Chern numbers, surface states are topologically protected in double gyroid photonic crystals with parity breaking symmetry. The angle resolved characterization method could be utilize to resolve both Weyl points and surface states. Chapter 4 depicts design, fabrication, and characterization of Dirac-like surface plasmon dispersions in metallic nano-pillars. Chapter 5 presents experimental investigation
of coupled silicon Mie resonators, which is the first step towards topological design based on inter-lattice sites coupling in the next chapter. Chapter 6 details photonic bandstructure from angle-resolved cathodoluminescence measurements. We analyze bandstructures collected from the bulk of trivially and topologically gapped lattices, as well as zigzag and arm-chaired edges of domain boundaries. Chapter 7 outlines a method to optically enhance dissociation of hydrazine molecules using ultraviolet plasmons, and attempts to use this method for low temperature GaN growth.</p>https://resolver.caltech.edu/CaltechTHESIS:09112017-095117655Numerical Methods for Many-Body Quantum Dynamics
https://resolver.caltech.edu/CaltechTHESIS:05292019-112014488
Year: 2019
DOI: 10.7907/VC0P-3K15
<p>This thesis describes two studies of the dynamics of many-body quantum systems with extensive numerical support.</p>
<p>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.</p>
<p>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.</p>
<p>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 <i>not</i> thermalize. We then show that these engines still have high efficiency when run at finite speed, and we compare to competitor engines.</p>
https://resolver.caltech.edu/CaltechTHESIS:05292019-112014488Reducing Computational Costs for Many-Body Physics Problems
https://resolver.caltech.edu/CaltechTHESIS:05112021-235754667
Year: 2021
DOI: 10.7907/xpvv-ar02
<p>Three different computational physics problems are discussed. The first project is solving the semi-classical Boltzmann transport equation (BTE) to compute the thermal conductivity of 1-D superlattices. We consider various spectral scattering models at each interface. This computation requires the inversion of a matrix whose size scales with the number of points used in the discretization of the Brillouin zone. We use spatial symmetries to reduce the size of data points and make the computation manageable. The other two projects involve quantum systems. Simulating quantum systems can potentially require exponential resources because of the exponential scaling of Hilbert space with system size. However, it has been observed that many physical systems, which typically exhibit locality in space or time, require much fewer resources to accurately simulate within some small error tolerance. The second project in the thesis is a two-step factorization of the electronic structure Hamiltonian that allows for efficient implementation on a quantum computer and also systematic truncation of small contributions. By using truncations that only incur errors below chemical accuracy, one is able to reduce the number of terms in the Hamiltonian from <i>O</i>(<i>N</i>⁴) to <i>O</i>(<i>N</i>³), where <i>N</i> is the number of molecular orbitals in the system. The third project is a tensor network algorithm based on the concept of influence functionals (IFs) to compute long-time dynamics of single-site observables. IFs are high-dimensional objects that describe the influence of the bath on the dynamics of the subsystem of interest over all times, and we are interested in their low-rank approximations. We study two numerical models, the spin-boson model and a model of interacting hard-core bosons in a 1D harmonic trap, and find that the IFs can be efficiently computed and represented using tensor network methods. Consistent with physical intuition, the correlations in the IFs appear to decrease with increased bath sizes, suggesting that the low-rank nature of the IF is due to nontrivial cancellations in the bath.</p>https://resolver.caltech.edu/CaltechTHESIS:05112021-235754667A Very Wide Bandwidth SIS Heterodyne Receiver Design for Millimeter and Submillimeter Astronomy
https://resolver.caltech.edu/CaltechTHESIS:09062020-111601302
Year: 2021
DOI: 10.7907/357d-6535
<p>This text describes in some detail the design and operational history of an instrument used as the front-end receiver for a fast, broadband, high-resolution spectrometer for the 1.3 millimeter wavelength atmospheric window. Using only a single superconductor-insulator-superconductor (SIS) tunnel junction as its heterodyne detector, the receiver’s novel design achieved then unprecedented RF and IF bandwidths and incorporated several innovations which have since been widely adopted within the millimeter and submillimeter wave research communities. Although intended as a relatively simple technology demonstrator and starting point for more refined and sophisticated designs, the receiver turned out to be a useful astronomical instrument in its own right, and it was deployed as a de facto facility instrument for several years at the Caltech Submillimeter Observatory. Also described are the author’s contributions to another important aid to research and design efforts: the <i>SuperMix</i> software library for the analysis and optimization of high-frequency circuitry, especially developed to aid in the design of systems involving SIS and other superconducting elements. Finally, the text may serve as a useful introduction to the theory behind and methodology for modeling and design of SIS heterodyne mixers.</p>https://resolver.caltech.edu/CaltechTHESIS:09062020-111601302New Tensor Network Methods and Studies of Criticality in Low-Dimensional Quantum Systems
https://resolver.caltech.edu/CaltechTHESIS:05122021-000037101
Year: 2021
DOI: 10.7907/vhwq-gz88
Several investigations are presented around the general topic of the ground state and low-energy behavior of models for many-body quantum physics in one dimension (1d). We develop a novel numerical method for the ground and low-energy sectors of local Hamiltonians in 1d which is based on proofs from quantum information theory. This method, the rigorous renormalization group (RRG), enjoys the benefits of explicit global information from the Hamiltonian in its local step, allowing it to avoid spurious convergence in systems with challenging energy landscapes. We apply RRG to the random XYZ spin chain in an unbiased numerical study evaluating infinite-randomness fixed point physics and continuously varying critical exponents in the ground state, finding evidence for both. In a related effective model with correlations preventing the exact solution of the strong-disorder renormalization group equations, we use the framework of random walks to rigorously establish continuously varying critical exponents. We also perform detailed studies of deconfined quantum critical points (DQCP) in 1d, providing strong evidence for phase transitions which display similar phenomenology to the canonical examples in 2d. A family of DQCP phase transitions in 1d is exhibited which appears to controlled by complex fixed points corresponding to a walking scenario for renormalization group flows.https://resolver.caltech.edu/CaltechTHESIS:05122021-000037101Light Induced Dynamics in Quantum Matter
https://resolver.caltech.edu/CaltechTHESIS:06072021-061251562
Year: 2021
DOI: 10.7907/a8z1-5c40
<p>This thesis presents studies of different schemes to probe and manipulate quantum matter using light with an aim to discover novel routes to efficiently control the properties of quantum materials. A special focus is placed on developing new schemes utilizing light-matter interactions (1) to modify exchange interactions in magnetic insulators, and (2) to probe and modify band topology in quantum matter.</p>
<p>In part II, new schemes are presented to probe local band topology of Bloch bands. First, we study the effects of time-dependent band topology on adiabatic evolution of a Bloch wavepacket. We find that it results in an electric-field analog in semi-classical equation of motion, and can be demonstrated in a honeycomb lattice by varying the sublattice offset energy. We then extend these methods to include non-adiabatic processes, and found interesting connections between the anomalous drift during band excitation and a quantum geometric quantity known as shift-vector. We generalize the concept of shift-vector to include different kinds of band transition protocols beyond light-induced dipole transitions. The idea of electric-field analog and the shift-vector are then combined to develop a novel charge pumping scheme. Motivated by these interesting consequences of band topology in non-adiabatic processes, we study shift-current response in moiré materials, and find that the highly topological nature of flat bands along with their very large unit cells significantly enhances these shift-vector related effects. This response also displays a strong dependence on interaction-induced changes in the band structure and quantum geometric quantities. These results suggest that shift-current response can possibly serve as a very reliable probe for interactions in twisted bilayer graphene. In addition to studying consequences of band topology on single-particle transport, we also consider Berry curvature effects on exciton transport. We find that the non-trivial band topology of underlying electron and hole bands allows us to manipulate excitons with a uniform electric field. We examine the conditions necessary to observe such transport and propose that transition metal dichalcogenide heterobilayers with moiré structure can prove an ideal platform for these effects.</p>
<p>In part III, we propose novel drive protocols based on manipulating orbital and lattice degrees of freedom in quantum materials with light. We found that light induced changes in orbital hybridization and their electronic energies results in a significant change in exchange interactions in quantum magnets. We also accounted for the role of ligands in periodically driven quantum magnets, and found that the predictions made by the minimal model based on direct-hopping can be wrong in certain regimes of drive parameters. This understanding of light induced modifications in ligand-mediated exchange interactions was used to explain the phase shift observed in coherent phonon oscillations of CrSiTe₃ upon the onset of short-range spin correlations. We also demonstrate that light induced coherent lattice vibrations can provide a new route to realize space-time symmetry protected topological phases. Our results suggest that manipulating additional degrees of freedom (not included in commonly employed minimal models of periodically driven systems) with light can provide novel routes for ultrafast control of quantum materials.</p>https://resolver.caltech.edu/CaltechTHESIS:06072021-061251562A Spectroscopic Study of Electronic Correlations in Twisted Bilayer Graphene by Scanning Tunneling Microscopy
https://resolver.caltech.edu/CaltechTHESIS:09242021-222116257
Year: 2022
DOI: 10.7907/ajgk-7246
<p>Twisted bilayer graphene around the magic angle has shown variety of correlated phases such as superconductivity, correlated insulators, and magnetism due to its flat band structure. The unconventional nature of the superconductivity and its pos- sible relation to high temperature superconductors have sparked a lot of theoretical and experimental efforts to understand the properties of the magic angle twisted bilayer graphene. While electrical transport measurements revealed the interesting phases, spectroscopic understanding is strongly needed to connect the phases with theoretical calculations. We present the spectroscopic studies of gate-tunable magic angle twisted bilayer graphene using scanning tunneling microscopy. We report that the band structure is significantly modified even at charge neutrality due to exchange interaction. We apply a perpendicular magnetic field and develop a novel method that enables scanning tunneling microscopy to reveal Landau fan diagrams. We discover topologically non-trivial states appearing at finite magnetic field, and from spectroscopy we are able to identify the mechanism. Finally, we verify inter- action driven band flattening experimentally in twisted bilayer graphene, which is responsible for creating strong correlations.</p>https://resolver.caltech.edu/CaltechTHESIS:09242021-222116257Two-Dimensional Transition Metal Dichalcogenides for Ultrathin Solar Cells
https://resolver.caltech.edu/CaltechTHESIS:04082022-171550192
Year: 2022
DOI: 10.7907/xrxk-3q08
<p>Ultrathin solar cells, with absorber layers less than one micron thick, have the potential to use orders of magnitude less high-quality semiconducting material than current silicon solar cells. This could be advantageous in applications that require high power output per unit weight, such as vehicle-integrated photovoltaics, or where reducing the capital cost of solar cell manufacturing is important. Transition metal dichalcogenides are a promising candidate for the semiconducting absorber layer of ultrathin solar cells due to their intrinsically passivated surfaces and their high absorption per unit thickness. </p>
<p>This thesis explores two-dimensional transition metal dichalcogenides for ultrathin photovoltaics. We start with the simplest type of solar cell, which collects carriers via a Schottky junction formed by sandwiching the absorber layer between two metal contacts with different work functions. To enable this geometry and avoid Fermi-level pinning, we develop a new process for gently transferring van der Waals metal contacts onto transition metal dichalcogenides. We measure an open-circuit voltage of 250 mV and a power conversion efficiency of 0.5% in Schottky-junction solar cells. To improve upon this efficiency, we next make carrier-selective contact solar cells, which employ wide bandgap semiconductors to selectively collect electrons on one side and holes on the other side of the absorber layer. We measure an open-circuit voltage of 520 mV and a power conversion efficiency greater than 2% in devices based on perovskite solar cell geometries, with PTAA and C60 as selective contact layers. We demonstrate that short carrier lifetimes limit the voltage in these solar cells to 750 mV, well below the detailed balance voltage limit. This motivates a more thorough understanding of the carrier dynamics at play, and we use a new pump-probe optical microscopy technique, stroboSCAT, to spatiotemporally track heat and carrier evolution in transition metal dichalcogenides. When paired with a kinetic model, we show that this technique can be used to measure lifetimes and other important material parameters even in materials with low radiative efficiencies.</p>
<p>We conclude by outlining future research directions towards achieving power conversion efficiencies greater than 10% in transition metal dichalcogenide solar cells.</p>https://resolver.caltech.edu/CaltechTHESIS:04082022-171550192Interface Optimization for Improved Photovoltaic Devices
https://resolver.caltech.edu/CaltechTHESIS:06022022-002941282
Year: 2022
DOI: 10.7907/kxdy-h496
<p>The wide band gaps and superior conductivity of ZnSₓSe₁₋ₓ semiconductors to amorphous Si suggest an alternative carrier-selective contact in silicon heterojunction solar cells. Electron-selective ZnSₓSe₁₋ₓ front contacts on p-type c-Si solar cells are explored by simulating in Sentaurus TCAD a large design parameter space informed by experimentally determined optoelectronic properties. Comparable performance to experimental and simulated p-SHJ reference devices is shown, with a champion simulated device efficiency of 20.8%. X-ray photoelectron spectroscopy is used to measure band offsets at interfaces for the aforementioned ZnSₓSe₁₋ₓ-c-Si photovoltaic devices as well as various carrier-selective contacts and passivation layers for GaAs photovoltaic devices.</p>https://resolver.caltech.edu/CaltechTHESIS:06022022-002941282Ultrafast Optical Control of Order Parameters in Quantum Materials
https://resolver.caltech.edu/CaltechTHESIS:08292022-044824279
Year: 2023
DOI: 10.7907/yxa0-6884
<p>Developing protocols to realize quantum phases that are not accessible thermally and to manipulate material properties on demand is one of the central problems of modern condensed matter physics. Impulsive electromagnetic stimulus provides an extensive playground not only to exert desired control over the material macroscopic properties but also to optically detect the underlying microscopic mechanisms. Two indispensable components form the cornerstone to realize these goals: a meticulous comprehension of light-induced phenomena and a suitable and versatile platform. </p>
<p>Abundant photoinduced phenomena emerge upon light irradiation. A collective oscillation of order parameter can be launched and probed in the weak perturbation regime; further increasing light intensity can transiently modulate the free-energy landscape, inducing a suppression, enhancement, reversal, and switch of order parameters; in the strong non-perturbative excitation regime, the system can be driven nonlinearly with microscopic coupling parameters modified. Understanding these light driven emergent phenomena lays the foundation of optical control and novel functionalities.</p>
<p>Quantum materials, embodying a large portfolio of topological and strongly correlated compounds, afford an exceptional venue to realize optical control. Owing to the complex interplay between the charge, spin, orbital, and lattice degrees of freedom, a rich phase diagram can be generated with various phases that are selectively and independently accessible via optical perturbations. They hence offer a wealth of opportunities to not only improve our comprehension of the underlying physics but also develop the next generation of ultrafast technologies.</p>
<p>In Chapter I of this thesis, I will first cover a multitude of light-induced emergent phenomena in quantum materials under the framework of time-dependent Landau theory, Keldysh theory, and Floquet theory, and then introduce several canonical microscopic models to quantitatively rationalize the intra- and interactions between different degrees of freedom in quantum materials. As the necessary theoretical background is established, three main experimental techniques that have been extensively utilized in my research: time-resolved reflectivity and Kerr effect, time-resolved second harmonic generation rotational anisotropy, and coherent phonon spectroscopy will be introduced in Chapter II. In Chapter III, I will demonstrate that a light-induced topological phase transition can be engendered concomitant with an inverse-Peierls structural phase transition in elemental Te. In Chapter IV, I will describe signatures of ultrafast reversal of excitonic order in excitonic insulator candidate Ta<sub>2</sub>NiSe<sub>5</sub> and substantiate a manipulation of the reversal as well as the Higgs mode with tailored light pulses. In Chapter V, a light-induced switch of spin-orbit-coupled quadrupolar order in multiband Mott insulator Ca<sub>2</sub>RuO<sub>4</sub> will be introduced. In Chapter VI, a Keldysh tuning of nonlinear carrier excitation and Floquet bandwidth renormalization in strongly driven Ca<sub>2</sub>RuO<sub>4</sub> will be covered.</p>https://resolver.caltech.edu/CaltechTHESIS:08292022-044824279Superconducting Circuit Architectures Based on Waveguide Quantum Electrodynamics
https://resolver.caltech.edu/CaltechTHESIS:03112023-174134421
Year: 2023
DOI: 10.7907/c7d8-nn87
<p>Quantum science and technology provides new possibilities in processing information, simulating novel materials, and answering fundamental questions beyond the reach of classical methods. Realizing these goals relies on the advancement of physical platforms, among which superconducting circuits have been one of the leading candidates offering complete control and read-out over individual qubits and the potential to scale up. However, most circuit-based multi-qubit architectures only include nearest-neighbor (NN) coupling between qubits, which limits the efficient implementation of low-overhead quantum error correction and access to a wide range of physical models using analog quantum simulation.</p>
<p>This challenge can be overcome by introducing non-local degrees of freedom. For example, photons in a shared channel between qubits can mediate long-range qubit-qubit coupling arising from light-matter interaction. In addition, constructing a scalable architecture requires this channel to be intrinsically extensible, in which case a one-dimensional waveguide is an ideal structure providing the extensible direction as well as strong light-matter interaction.</p>
<p>In this thesis, we explore superconducting circuit architectures based on light-matter interactions in waveguide quantum electrodynamics (QED) systems. These architectures in return allow us to study light-matter interaction, demonstrating strong coupling in the open environment of a waveguide by employing sub-radiant states resulting from collective effects. We further engineer the waveguide dispersion to enter the topological photonics regime, exploring interactions between qubits that are mediated by photons with topological properties. Finally, towards the goals of quantum information processing and simulation, we settle into a multi-qubit architecture where the photon-mediated interaction between qubits exhibits tunable range and strength. We use this multi-qubit architecture to construct a lattice with tunable connectivity for strongly interacting microwave photons, synthesizing a quantum many-body model to explore chaotic dynamics. The architectures in this thesis introduce scalable beyond-NN coupling between superconducting qubits, opening the door to the exploration of many-body physics with long-range coupling and efficient implementation of quantum information processing protocols.</p>https://resolver.caltech.edu/CaltechTHESIS:03112023-174134421Non-Equilibrium Quantum Dynamics in a Disordered Ising Magnet
https://resolver.caltech.edu/CaltechTHESIS:12182023-202554036
Year: 2024
DOI: 10.7907/tm3k-yk55
The quantum two-level system, or “qubit,” is a simple platform that nonetheless displays fundamentally non-trivial quantum behavior. The rare-earth magnet LiHoF₄ is a natural physical representation of a system of coupled qubits. With its uncommonly high crystal anisotropy, LiHoF₄ can be mapped to the problem of the Ising model in a transverse field. However, while this Ising approximation can quantitatively predict much of the equilibrium behavior, quantum corrections, originating from off-diagonal terms in the dipolar interaction that generate quantum fluctuations, are crucial in driving non-equilibrium dynamics when subject to an external drive. Furthermore, quenched disorder can be introduced through chemical substitution, which, through the dipolar interaction, generates spatially random pinning fields, as well as internal transverse fields, which drive quantum fluctuations. Noise measurements on the disordered ferromagnet LiHo<sub>0.65</sub>Y<sub>0.35</sub>F<sub>4</sub> show critical behavior, whose statistics are driven from the underlying pinning distribution, while measurements on LiHo<sub>0.40</sub>Y<sub>0.60</sub>F<sub>4</sub> display non-critical behavior that can only be attributed to quantum co-tunneling processes. This is the first demonstration of crackling noise in a ferromagnet in the purely quantum regime. Furthermore, pump-probe susceptibility measurements on the decoupled cluster glass show the system being driven out of equilibrium with astonishingly weak drives, due to resonant transitions arising from off-diagonal dipolar terms σ<sub>i</sub><sup>z</sup> σ<sub>j</sub><sup>x</sup>. Non-linear sample response is observable in inelastic Raman scattering measurements, and these spin clusters also exhibit asymmetric Fano resonances with high Q-factors of ~10⁵. Quantum interference effects can be tuned to fully decouple one of the dressed states from the others, rendering the sample transparent to the drive. This is analogous to optical systems that display electromagnetically-induced transparency, but at 100 Hz frequencies!https://resolver.caltech.edu/CaltechTHESIS:12182023-202554036Topological Phenomena in Time-Multiplexed Resonator Networks
https://resolver.caltech.edu/CaltechTHESIS:12222023-012844057
Year: 2024
DOI: 10.7907/2dp5-eb41
<p>In 2008, the prediction that gyromagnetic photonic crystals could host analogs of the quantum Hall effect sparked a revolution in photonics, as it became apparent that the synergy between photonics and topological physics provides distinct opportunities for fundamental research and technological innovation. Since then, topological photonics has produced experimental realizations of numerous theories from topological condensed matter physics, while the inherent robustness of topological edge states has enabled novel devices like topological lasers and topological quantum sources. Despite this success, practical challenges limit the breadth of topological phenomena accessible to the existing experimental platforms for topological photonics. Therefore, to accelerate the pace of scientific discovery and to inspire the next generation of topological technologies, it is desirable to develop a platform that overcomes the limitations of traditional topological photonic architectures. In this thesis, I propose time-multiplexed resonator networks as a next-generation platform for topological photonics, and I present three experimental projects that demonstrate the diverse capabilities of this platform.</p>
<p>In the first project, I use a time-multiplexed resonator network to demonstrate topological dissipation, in which nontrivial topology is encoded in the dissipation spectrum of a resonator array. I show measurements of dissipative topological phenomena in one- and two-dimensions and discuss how topological dissipation can be used to design resonator arrays with topologically robust quality factors. In the second project, I adapt a time-multiplexed resonator network to realize a topological mode-locked laser, and I show that this laser can realize non-Hermitian topological phenomena that had not previously been demonstrated in topological photonics. Finally, I experimentally study the dynamics of cavity solitons in a topological resonator array. This project demonstrates a general technique for realizing cavity solitons in large arrays of coupled resonators, which has become a relevant challenge in the soliton community over the past several years.</p>https://resolver.caltech.edu/CaltechTHESIS:12222023-012844057