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A Caltech Library Repository Feedhttp://www.rssboard.org/rss-specificationpython-feedgenenFri, 08 Dec 2023 21:55:25 +0000Fidelity of Kane's Binary Gate
https://resolver.caltech.edu/CaltechTHESIS:01082018-144530428
Authors: Dani, Keshav Moreshwar
Year: 2000
DOI: 10.7907/w577-ys54
The physics of information and computation has been a recognized discipline for several decades. This is not surprising. Information is, after all, encoded in the state of a physical system. Our abilities to compute and process information depend directly on the physics of the system. A computation is something that can be carried out on an actual physically realizable device. Hence the study of information and computation is linked to the study of the underlying physical process. From the perspective of developing state-of-the-art computing technology, study of the principles of physics and material science is essential. From a more abstract and theoretical point of view, there have been noteworthy milestones in our understanding of how physics constrains our ability to use and manipulate information e.g. Landauer's Principle, Reversible Computation, Explanation of Maxwell's Daemon, etc.https://thesis.library.caltech.edu/id/eprint/10625From Sequence to Function through Secondary Structure Kinetics of RNA and DNA
https://resolver.caltech.edu/CaltechTHESIS:02132018-142852598
Authors: Meruelo, Alejandro Daniel
Year: 2006
DOI: 10.7907/4bxt-wa89
A number of efforts to determine function from sequence of RNA and DNA have
been made with varying success. Here we study the determination of function from
sequence of DNA and RNA through their secondary structure kinetics, specifically
the series of transitions between secondary structures. This series of transitions or
microscopic structure can be described by a system of ordinary differential equations
that can be approximating using balanced truncation to determine the macroscopic
structure. By doing so, we have been able to identify signature topological features of
microscopic structure and mathematically characterize the corresponding classes of
macroscopic structure. Thus we are now able to take large, complex systems, reduce
them, and understand their behavior. In the future, we hope to be able to identify
small microscopic changes that lead to large macroscopic changes and possibly phasetransition
like conditions between secondary states. Ultimately, this may lead to the
development of a secondary-structure kinetics theory describing how one or more
strands of DNA pair with one another to form different secondary structures and its
potential future experimental verification.https://thesis.library.caltech.edu/id/eprint/10718Magnetic Microtraps for Cavity QED, Bose-Einstein Condensates, and Atom Optics
https://resolver.caltech.edu/CaltechETD:etd-09202005-205733
Authors: Lev, Benjamin Leonard
Year: 2006
DOI: 10.7907/YP00-7Z87
<p>The system comprised of an atom strongly coupled to photons, known as cavity quantum electrodynamics (QED), provides a rich experimental setting for quantum information processing, both in the implementation of quantum logic gates and in the development of quantum networks. Moreover, studies of cavity QED will help elucidate the dynamics of continuously observed open quantum systems with quantum-limited feedback.</p>
<p>To achieve these goals in cavity QED, a neutral atom must be tightly confined inside a high-finesse cavity with small mode volume for long periods of time. Microfabricated wires on a substrate---known as an atom chip---can create a sufficiently high-curvature magnetic potential to trap atoms in the Lamb-Dicke regime. We have recently integrated an optical fiber Fabry-Perot cavity with such a device. The microwires allow the on-chip collection and laser cooling of neutral atoms, and allow the magnetic waveguiding of these atoms to an Ioffe trap inside the cavity mode. Magnetically trapped intracavity atoms have been detected with this cavity QED system. A similar experiment employing microdisks and photonic bandgap cavities is nearing completion. With these more exotic cavities, a robust and scalable atom-cavity chip system will deeply probe the strong coupling regime of cavity QED with magnetically trapped atoms.</p>
<p>Atom chips have found great success in producing and manipulating Bose-Einstein condensates and in creating novel atom optical elements. An on-chip BEC has been attained in a miniaturized system incorporating an atom chip designed for atom interferometry and for studies of Josephson effects of a BEC in a double-well potential.</p>
<p>Using similar microfabrication techniques, we created and demonstrated a specular magnetic atom mirror formed from a standard computer hard drive. This device, in conjunction with micron-sized charged circular pads, can produce a 1-D ring trap which may prove useful for studying Tonks gases in a ring geometry and for creating devices such as a SQUID-like system for neutral atoms.</p>
<p>This thesis describes the fabrication and employment of these atoms chips in experiments at both Caltech and Munich, the latter in collaboration with Professors Theodore Haensch and Jakob Reichel at the Max Planck Institute for Quantum Optics.</p>https://thesis.library.caltech.edu/id/eprint/3658Ultra-Sensitive Absorption Measurements through Cavity-Enhanced Spectroscopy
https://resolver.caltech.edu/CaltechETD:etd-09202008-110124
Authors: McGarvey, Raymond Timothy James
Year: 2006
DOI: 10.7907/CGYD-6J27
The desire to increase the sensitivity of solution-based absorption spectroscopy is motivated by the need for label-free biosensing (which provides a more authentic indication of the state of a biological system) and by the usefulness of characterizing the kinetics of biologically-relevant reactions (which may not be accurately characterizable at reagent concentrations required by standard methods. There are a number of techniques by which such increasingly sensitive measurements have been made, including cavity ringdown spectroscopy, incoherent cavity-enhanced spectroscopy, microsphere-based whispering-gallery mode sensing,and our cavity-enhanced measurements, which are the most sensitive to date and which can be conducted in real time with high bandwidth. Our current device has a demonstrated detection threshold of 1.7x 10^{-7}/sqrt{Hz} (4.36x10^{-6}cm^{-1}), which could with further technical work be improved to a shot-noise limited sensitivity of 1.93x 10^{-10}/sqrt{Hz} (1.06x10^{-8}cm^{-1}). The latter would correspond to an average of 700 strong absorbers (epsilon = 10^5 M^{-1}cm^{-1}) in the optical beam volume. The shot-noise limited detection threshold of our measurement method could potentially be improved by up to two orders of magnitude by incorporating state-of-the-art optical mirrors. With such mirrors, cavity-enhanced absorption experiments performed with gas-phase samples have previously demonstrated single molecule sensitivity. We have established that solution-based cavity-enhanced absorption measurements are more sensitive than standard single-pass measurements by the predicted enhancement factor for our present device (~ 20,000). These measurements provide the proof-of-principle for solution-based, cavity-enhanced spectroscopy and serve as the intermediate step towards the attainment of the theoretical sensitivity of this technique. We believe that this device will be of broad interest to the scientific community, because it is presently the most sensitive solution-based spectroscopic device. It can make real-time absorption measurements which would allow monitoring of the kinetics of chemical reactions in which the spectral properties of reactants change by even a small amount, and, near its theoretical limit of sensitivity (given currently available mirrors), such a device could potentially resolve single-molecule absorption events on the sub-millisecond timescale and below.
https://thesis.library.caltech.edu/id/eprint/3671Continuous Quantum Measurement of Cold Alkali-Atom Spins
https://resolver.caltech.edu/CaltechETD:etd-02172007-172548
Authors: Stockton, John Kenton
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://thesis.library.caltech.edu/id/eprint/667Feedback Control of Brownian Motion for Single-Particle Fluorescence Spectroscopy
https://resolver.caltech.edu/CaltechETD:etd-10092006-165831
Authors: Berglund, Andrew John
Year: 2007
DOI: 10.7907/EBKX-BP40
The stochastic Brownian motion of individual particles in solution constrains the utility of single-particle fluorescence microscopy both by limiting the dwell time of particles in the observation volume and by convolving their internal degrees of freedom with their random spatial trajectories. This thesis describes the use of active feedback control to eliminate these undesirable effects. We designed and implemented a feedback tracking system capable of locking the position of a fluorescent particle to the optic axis of our microscope, i.e., capable of tracking the two-dimensional, planar Brownian motion of a free particle in solution. A full theoretical description of the experiment is given in the language of linear stochastic control theory. The model describes both the statistics of the tracking system and provides a generalization of the theory of open-loop Fluorescence Correlation Spectroscopy (FCS) that accounts for fluctuations in fluorescence arising from competition between diffusion and damping. We find excellent agreement between theory and experiment. Using fluorescent polymer microspheres as test particles, we find that the observation time for these particles can be increased by 2-3 orders of magnitude over the open-loop scenario. The system achieves nearly optimal performance for moderately fast-moving particles at very low fluorescent count rates, comparable to those of a single fluorescent protein molecule. The system can classify particles in a binary mixture based on a real-time estimate of their diffusion coefficients (differing by a factor of ~4), achieving 90% success using fewer than 600 photons detected over 120 ms. Future directions for both the experimental and theoretical techniques are briefly discussed.https://thesis.library.caltech.edu/id/eprint/3996An Ab Initio Approach to the Inverse Problem-Based Design of Photonic Bandgap Devices
https://resolver.caltech.edu/CaltechETD:etd-05242007-160527
Authors: Au, John King-Tai
Year: 2007
DOI: 10.7907/TZG8-R064
We present an ab inito treatment of the inverse photonic bandgap (or photonic crystal) device design problem. Using first principles, we derive the two-dimensional inverse Helmholtz equation that solves for the dielectric function that supports a given electromagnetic field with the desired properties. We show that the problem is ill-posed, meaning a solution often does not exist for the design problem. Our work elucidates fundamental limits to any inverse problem based design approach for arbitrary and optimal design of photonic devices. Despite these severe limitations, we achieve remarkable success in two design problems of particular importance to atomic physics applications, but also of general importance to the rest of the photonic community. As the first demonstration of our technique, we arbitrarily design the full dispersion curve of a photonic crystal waveguide. Dispersion control is important for maintaining the shape of pulses as they propagate along the waveguide. For our second demonstration, we take a point defect photonic crystal cavity in the nominal acceptor configuration (where the central defect has a lower index of refraction than the bulk material) and force it into the donor configuration (where the defect has a higher index of refraction than the bulk material), while requiring that the electromagnetic field maintain the properties of the acceptor mode. We were able to cross over this threshold while retaining a 93.6 percent overlap with the original mode.https://thesis.library.caltech.edu/id/eprint/2026Filtering, Stability, and Robustness
https://resolver.caltech.edu/CaltechETD:etd-12122006-164640
Authors: van Handel, Ramon
Year: 2007
DOI: 10.7907/4p53-1h42
<p>The theory of nonlinear filtering concerns the optimal estimation of a Markov signal in noisy observations. Such estimates necessarily depend on the model that is chosen for the signal and observations processes. This thesis studies the sensitivity of the filter to the choice of underlying model over long periods of time, within the framework of continuous time filtering with white noise type observations.</p>
<p>The first topic of this thesis is the asymptotic stability of the filter, which is studied using the theory of conditional diffusions. This leads to improvements on pathwise stability bounds, and to new insight into existing stability results in a fully probabilistic setting. Furthermore, I develop in detail the theory of conditional diffusions for finite-state Markov signals and clarify the duality between estimation and stochastic control in this context.</p>
<p>The second topic of this thesis is the sensitivity of the nonlinear filter to the model parameters of the signal and observations processes. This section concentrates on the finite state case, where the corresponding model parameters are the jump rates of the signal, the observation function, and the initial measure. The main result is that the expected difference between the filters with the true and modified model parameters is bounded uniformly on the infinite time interval, provided that the signal process satisfies a mixing property. The proof uses properties of the stochastic flow generated by the filter on the simplex, as well as the Malliavin calculus and anticipative stochastic calculus.</p>
<p>The third and final topic of this thesis is the asymptotic stability of quantum filters. I begin by developing quantum filtering theory using reference probability methods. The stability of the resulting filters is not easily studied using the preceding methods, as smoothing violates the nondemolition requirement. Fortunately, progress can be made by randomizing the initial state of the filter. Using this technique, I prove that the filtered estimate of the measurement observable is stable regardless of the underlying model, provided that the initial states are absolutely continuous in a suitable sense.</p>https://thesis.library.caltech.edu/id/eprint/4971Feedback Tracking and Correlation Spectroscopy of Fluorescent Nanoparticles and Biomolecules
https://resolver.caltech.edu/CaltechETD:etd-05072008-204627
Authors: McHale, Kevin L.
Year: 2008
DOI: 10.7907/6YYA-9T10
<p>The best way to study dynamic fluctuations in single molecules or nanoparticles is to look at only one particle at a time, and to look for as long as possible. Brownian motion makes this difficult, as molecules move along random trajectories that carry them out of any fixed field of view. We developed an instrument that tracks the Brownian motion of single fluorescent molecules in three dimensions and in real-time while measuring fluorescence with nanosecond time resolution and single-photon sensitivity. The apparatus increases observation times by approximately three orders of magnitude while improving data-collecting efficiency by locking tracked objects to a high-intensity region of the excitation laser.</p>
<p>As a first application of our technique, we tracked and studied the fluorescence statistics of semiconductor quantum dots. Our measurements were well resolved at 10ns correlation times, allowing measurement of photon anti-bunching on single particles in solution for the first time. We observed variations of (34 ± 16)% in the fluorescence lifetimes and (23 ± 18)% in the absorption cross-sections within an aqueous quantum dot sample, confirming that these variations are real, not artifacts of the immobilization methods previously used to study them. Additionally, we studied quantum dot fluorescence intermittency and its dependence on 2-mercaptoethanol, finding evidence that the chemical suppresses blinking on short time-scales (<1s) by reducing the lifetime of the dark state.</p>
<p>Finally, we studied the translational and intramolecular Brownian motion of λ-phage DNA molecules. Our apparatus decouples these motions almost completely, and yielded a translational diffusion coefficient estimate D=(0.71 ± 0.05)μm²/s lying between previous measurements for this molecule under identical solution conditions but with less precise techniques. Our measurements show clear evidence of intramolecular motion of the polymer chain in the form of statistical correlations on time-scales up to 1s, but we have not yet been able to determine the influence of solvent interactions on these dynamics.</p>
https://thesis.library.caltech.edu/id/eprint/1667Reduced Order Models for Open Quantum Systems
https://resolver.caltech.edu/CaltechETD:etd-11182008-113904
Authors: Hopkins, Asa Sies
Year: 2009
DOI: 10.7907/KPS7-9C05
Many quantum mechanical systems require large (potentially infinite) numbers of variables to exactly describe their state. In this thesis, I examine two approaches to develop simple, approximate models for such systems, which capture their essential dynamics. I use two bistable regimes of the Jaynes-Cummings model of cavity quantum electrodynamics as example systems to evaluate the effectiveness of each approach. In the phase bistable regime (which occurs with large driving field, and which I study in an on-resonance "bad cavity" regime to make numerical simulations tractable), the cavity field switches between two states with identical amplitude but opposite phase. In the absorptive bistable regime (which I study with small driving field in an on-resonance "good cavity"'), two stable regions of state space differ in cavity field amplitude as well as their shape and qualitative behavior. After introducing these two regimes and their dynamics, I give a short introduction to projecting dynamical equations onto linear subspaces. Proper Orthogonal Decomposition (POD) allows the algorithmic construction of subspaces onto which the dynamics may be projected. I demonstrate that the application of POD to phase bistability results in effective approximate filters, while the asymmetry of the absorptive bistable case requires extensions to POD, developed in this thesis, to create a functional filter. Local Tangent Space Alignment is one of a class of unsupervised manifold learning algorithms which use the local geometry of high-dimensional data, such as quantum trajectories, to calculate the coordinates of that data on a low-dimensional manifold. I show how this algorithm functions, and characterize the manifolds that result from phase and absorptive bistability. I fit the 3-dimensional phase bistable manifold with a small set of system observables, and create a three-dimensional set of equations (similar to the semi-classical Maxwell-Bloch equations) which perform very well as a filter. Absorptive bistability again proves to be more complicated, but I am able to show that the underlying manifold is small, and make some progress on characterizing its relations with system observables.
https://thesis.library.caltech.edu/id/eprint/4599Bifurcations in Single Atom Cavity QED
https://resolver.caltech.edu/CaltechETD:etd-05262009-100436
Authors: Armen, Michael A.
Year: 2009
DOI: 10.7907/2G57-2609
Current research in single-atom cavity quantum electrodynamics largely emphasizes the input-output properties of strongly coupled systems, from normal mode splitting to photon blockade. But over the last decade, experiments have, with few exceptions, focused on relatively weak driving conditions. This thesis concentrates on a range of quantum nonlinear phenomena in the strong driving regime. In particular, I discuss the observation of random-telegraph phase switching in the light transmitted through a Fabry-Perot resonator containing one strongly coupled atom and 10-100 photons, confirming long-standing predictions of a phenomenon known as single-atom phase bistability. These results highlight the relevance of cavity quantum electrodynamics in the development of attojoule nanophotonic logic and signal processing. In addition, I consider a general class of bifurcation phenomena that are manifest within this physical setting. Here, focus is placed on the investigation of quantum-classical correspondence near semiclassical bifurcation points. https://thesis.library.caltech.edu/id/eprint/2119