College of Computer, Mathematical & Natural Sciences
http://hdl.handle.net/1903/12
2020-07-11T01:31:48ZNumerical Studies of Quantum Chaos in Various Dynamical Systems
http://hdl.handle.net/1903/26199
Numerical Studies of Quantum Chaos in Various Dynamical Systems
Rozenbaum, Efim
We study two classes of quantum phenomena associated with classical chaos in a variety of quantum models: (i) dynamical localization and its extension and generalization to interacting few- and many-body systems and (ii) quantum exponential divergences in high-order correlators and other diagnostics of quantum chaos.
Dynamical localization (DL) is a subtle phenomenon related to Anderson localization. It hinges on quantum interference and is typically destroyed in presence of interactions. DL often manifests as a failure of a driven system to heat up, violating the foundations of statistical physics. Kicked rotor (KR) is a prototypical chaotic classical model that exhibits linear energy growth with time. The quantum kicked rotor (QKR) features DL instead: its energy saturates. Multiple attempts of many-body generalizations faced difficulties in preserving DL. Recently, DL was shown in a special integrable many-body model. We study non-integrable models of few- and many-body QKR-like systems and provide direct evidence that DL can persist there. In addition, we show how a novel related concept of localization landscape can be applied to study transport in rippled channels.
Out-of-time-ordered correlator (OTOC) was proposed as an indicator of quantum chaos, since in the semiclassical limit, this correlator's possible exponential growth rate (CGR) resembles the classical Lyapunov exponent (LE). We show that the CGR in QKR is related, but distinct from the LE in KR. We also show a singularity in the OTOC at the Ehrenfest time tᴱ due to a delay in the onset of quantum interference. Next, we study scaling of OTOC beyond tᴱ. We then explore how the OTOC-based approach to quantum chaos relates to the random-matrix-theoretical description by introducing an operator we dub the Lyapunovian. Its level statistics is calculated for quantum stadium billiard, a seminal model of quantum chaos, and aligns perfectly with the Wigner-Dyson surmise. In the semiclassical limit, the Lyapunovian reduces to the matrix of uncorrelated finite-time Lyapunov exponents, connecting the CGR at early times, when the quantum effects are weak, to universal level repulsion that hinges on strong quantum interference. Finally, we consider quantum polygonal billiards: their classical counterparts are non-chaotic. We show exponential growth of the OTOCs in these systems, sharply contrasted with the classical behavior even before quantum interference develops.
2020-01-01T00:00:00ZMixed-Species Ion Chains for Quantum Networks
http://hdl.handle.net/1903/26198
Mixed-Species Ion Chains for Quantum Networks
Sosnova, Ksenia
Quantum computing promises solutions to some of the world's most important problems that classical computers have failed to address. The trapped-ion-based quantum computing platform has a lot of advantages for doing so: ions are perfectly identical and near-perfectly isolated, feature long coherent times, and allow high-fidelity individual laser-controlled operations. One of the greatest remaining obstacles in trapped-ion-based quantum computing is the issue of scalability. The approach that we take to address this issue is a modular architecture: separate ion traps, each with a manageable number of ions, are interconnected via photonic links. To avoid photon-generated crosstalk between qubits and utilize advantages of different kinds of ions for each role, we use two distinct species - ¹⁷¹Yb⁺ as memory qubits and ¹³⁸Ba⁺ as communication qubits. The qubits based on ¹⁷¹Yb⁺ are defined within the hyperfine "clock" states characterized by a very long coherence time while ¹³⁸Ba⁺ ions feature visible-range wavelength emission lines. Current optical and fiber technologies are more efficient in this range than at shorter wavelengths.
We present a theoretical description and experimental demonstration of the key elements of a quantum network based on the mixed-species paradigm. The first one is entanglement between an atomic qubit and the polarization degree of freedom of a pure single photon. We observe a value of the second-order correlation function g⁽²⁾(0) = (8.1 ± 2.3)⨉10⁻⁵ without background subtraction, which is consistent with the lowest reported value in any system. Next, we show mixed-species entangling gates with two ions using the Mølmer-Sørensen and Cirac-Zoller protocols. Finally, we theoretically generalize mixed-species entangling gates to long ion chains and characterize the roles of normal modes there. In addition, we explore sympathetic cooling efficiency in such mixed-species crystals. Besides these developments, we demonstrate new techniques for manipulating states within the D₃⸝₂-manifold of zero-nuclear-spin ions - a part of a protected qubit scheme promising seconds-long coherence times proposed by Aharon et al. in 2013. As a next step, we provide a detailed description of the protocols for three- and four-node networks with mixed species, along with a novel design for the third trap with in-vacuum optics to optimize light collection.
2020-01-01T00:00:00ZUNCOVERING PATTERNS IN COMPLEX DATA WITH RESERVOIR COMPUTING AND NETWORK ANALYTICS: A DYNAMICAL SYSTEMS APPROACH
http://hdl.handle.net/1903/26197
UNCOVERING PATTERNS IN COMPLEX DATA WITH RESERVOIR COMPUTING AND NETWORK ANALYTICS: A DYNAMICAL SYSTEMS APPROACH
Krishnagopal, Sanjukta
In this thesis, we explore methods of uncovering underlying patterns in complex data, and making predictions, through machine learning and network science.
With the availability of more data, machine learning for data analysis has advanced rapidly. However, there is a general lack of approaches that might allow us to 'open the black box'. In the machine learning part of this thesis, we primarily use an architecture called Reservoir Computing for time-series prediction and image classification, while exploring how information is encoded in the reservoir dynamics.
First, we investigate the ways in which a Reservoir Computer (RC) learns concepts such as 'similar' and 'different', and relationships such as 'blurring', 'rotation' etc. between image pairs, and generalizes these concepts to different classes unseen during training. We observe that the high dimensional reservoir dynamics display different patterns for different relationships. This clustering allows RCs to perform significantly better in generalization with limited training compared with state-of-the-art pair-based convolutional/deep Siamese Neural Networks.
Second, we demonstrate the utility of an RC in the separation of superimposed chaotic signals. We assume no knowledge of the dynamical equations that produce the signals, and require only that the training data consist of finite time samples of the component signals. We find that our method significantly outperforms the optimal linear solution to the separation problem, the Wiener filter.
To understand how representations of signals are encoded in an RC during learning, we study its dynamical properties when trained to predict chaotic Lorenz signals. We do so by using a novel, mathematical fixed-point-finding technique called directional fibers. We find that, after training, the high dimensional RC dynamics includes fixed points that map to the known Lorenz fixed points, but the RC also has spurious fixed points, which are relevant to how its predictions break down.
While machine learning is a useful data processing tool, its success often relies on a useful representation of the system's information. In contrast, systems with a large numbers of interacting components may be better analyzed by modeling them as networks. While numerous advances in network science have helped us analyze such systems, tools that identify properties on networks modeling multi-variate time-evolving data (such as disease data) are limited. We close this gap by introducing a novel data-driven, network-based Trajectory Profile Clustering (TPC) algorithm for 1) identification of disease subtypes and 2) early prediction of subtype/disease progression patterns. TPC identifies subtypes by clustering patients with similar disease trajectory profiles derived from bipartite patient-variable networks. Applying TPC to a Parkinson’s dataset, we identify 3 distinct subtypes. Additionally, we show that TPC predicts disease subtype 4 years in advance with 74% accuracy.
2020-01-01T00:00:00ZELECTROCHEMISTRY OF PRECISION NANOSTRUCTURES FOR HIGH PERFORMANCE ENERGY STORAGE DEVICES
http://hdl.handle.net/1903/26192
ELECTROCHEMISTRY OF PRECISION NANOSTRUCTURES FOR HIGH PERFORMANCE ENERGY STORAGE DEVICES
Kim, Nam
With the increase in the demand for high performing energy storage devices, the energy storage community has explored ways to improve Li-ion battery chemistry. Previous research has demonstrated that nanostructuring of Li-ion electrodes enables significant improvements in their power and energy densities. However, a systematic study is needed to quantify the impact of specific structural properties on the electrochemical behavior of the nanostructured electrode and to develop a guideline for high performance energy storage devices. In the first study of this dissertation, we investigate the impact of pore diameter, dynamic conductivity and interconnected structures on the electrochemistry of V2O5, cathode material for Li ion batteries. We determined that there were positive and negative effects of the interconnected structure depending on the material properties. When V2O5’s electronic conductivity increased with the degree of lithiation, a higher power density was measured with more interconnections. When the material’s electronic conductivity decreased with lithiation, a lower power density was measured with more interconnections. In the second study, we employ microfabrication techniques and atomic layer deposition to fabricate well defined nanochannels to study the effect of electrolyte nanoconfinement on the electrochemistry of anatase TiO2. Surprisingly, nanoconfinement resulted in high energy and power densities when compared to the bulk material. Simulations showed that the improvement in the electrode behavior was due to the negative surface charges of TiO2 which resulted high local concentration of Li ions within the nanochannel and minimal loss in the driving potential was observed at the stern layer. In the third study, we fabricate a platform for high performance 3D solid state batteries on a Si wafer to study the effect of high aspect ratio nanostructures on the electrochemical behavior of thin film solid state batteries. The V2O5 electrode in 3D scaffold showed 113 times higher capacity than the planar electrode at 2μA/cm2 and 1333 times higher capacity at 0.5mA/cm2. These studies can help to understand key structural parameters for improved Li-ion batteries, and the test platforms we developed in these studies can be applied to increase understanding of structural impacts on other ion battery chemistries as well.
2020-01-01T00:00:00Z