Physics Department Theses and Dissertations

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Beyond the Exceptional Point: Exploring the Features of Non-Hermitian PT Symmetric Systems
(2022-08) Agarwal, Kaustubh Shrikant; Joglekar, Yogesh N.; Vemuri, Gautam; Ou, Zhe “Jeff”; Petrache, Horia I.; Lukens, Joseph M.
Over the past two decades, open systems that are described by a non-Hermitian Hamiltonian have become a subject of intense research. These systems encompass classical wave systems with balanced gain and loss, semi-classical models with mode selective losses, and lossy quantum systems. The rapidly growing research on these systems has mainly focused on the wide range of novel functionalities they demonstrate. In this thesis, I intend to present some intriguing properties of a class of open systems which possess parity (P) and time-reversal (T) symmetry with a theoretical background, accompanied by the experimental platform these are realized on. These systems show distinct regions of broken and unbroken symmetries separated by a special phase boundary in the parameter space. This separating boundary is called the PT-breaking threshold or the PT transition threshold. We investigate non-Hermitian systems in two settings: tight binding lattice models, and electrical circuits, with the help of theoretical and numerical techniques. With lattice models, we explore the PT-symmetry breaking threshold in discrete realizations of systems with balanced gain and loss which is determined by the effective coupling between the gain and loss sites. In one-dimensional chains, this threshold is maximum when the two sites are closest to each other or the farthest. We investigate the fate of this threshold in the presence of parallel, strongly coupled, Hermitian (neutral) chains, and find that it is increased by a factor proportional to the number of neutral chains. These results provide a surprising way to engineer the PT threshold in experimentally accessible samples. In another example, we investigate the PT-threshold for a one-dimensional, finite Kitaev chain—a prototype for a p-wave superconductor— in the presence of a single pair of gain and loss potentials as a function of the superconducting order parameter, onsite potential, and the distance between the gain and loss sites. In addition to a robust, non-local threshold, we find a rich phase diagram for the threshold that can be qualitatively understood in terms of the band-structure of the Hermitian Kitaev model. Finally, with electrical circuits, we propose a protocol to study the properties of a PT-symmetric system in a single LC oscillator circuit which is contrary to the notion that these systems require a pair of spatially separated balanced gain and loss elements. With a dynamically tunable LC oscillator with synthetically constructed circuit elements, we demonstrate static and Floquet PT breaking transitions by tracking the energy of the circuit. Distinct from traditional mechanisms to implement gain and loss, our protocol enables parity-time symmetry in a minimal classical system.
Exceptional Points and their Consequences in Open, Minimal Quantum Systems
(2022-08) Muldoon, Jacob E.; Joglekar, Yogesh; Decca, Ricardo; Cheng, Rui; Vemuri, Gautam; Cincio, Lukasz
Open quantum systems have become a rapidly developing sector for research. Such systems present novel physical phenomena, such as topological chirality, enhanced sensitivity, and unidirectional invisibility resulting from both their non-equilibrium dynamics and the presence of exceptional points. We begin by introducing the core features of open systems governed by non-Hermitian Hamiltonians, providing the PT -dimer as an illustrative example. Proceeding, we introduce the Lindblad master equation which provides a working description of decoherence in quantum systems, and investigate its properties through the Decohering Dimer and periodic potentials. We then detail our preferred experimental apparatus governed by the Lindbladian. Finally, we introduce the Liouvillian, its relation to non-Hermitian Hamiltonians and Lindbladians, and through it investigate multiple properties of open quantum systems.
Injection Current Modulated Parity-Time Symmetry in Coupled Semiconductor Lasers
(2021-08) Thomas, Luke; Vemuri, Gautam; Gavrin, Andrew; Petrache, Horia; Wassall, Stephen
This research investigates the characteristics of Parity Time symmetry breaking in two optically coupled, time delayed semiconductor lasers. A theoretical model is used to describe the controllable parameters in the experiment and intensity output of the coupled lasers. The PT parameters we control are the spatial separation between the two lasers, the frequency detuning, and the coupling strength. We find that the experimental data agrees with the predictions from the theoretical model confirming the intensity behaviors of the lasers, and the monotonic change in PT-threshold as a function of coupling scaled by the time delay
Investigation of PT Symmetry Breaking and Exceptional Points in Delay-coupled Semiconductor Lasers
(2021-08) Wilkey, Andrew; Vemuri, Gautam; Joglekar, Yogesh; Liu, Jing; Ou, Jeff; Petrache, Horia
This research investigates characteristics of PT (parity-time) symmetry breaking in a system of two optically-coupled, time-delayed semiconductor lasers. A theoretical rate equation model for the lasers' electric fields is presented and then reduced to a 2x2 Hamiltonian model, which, in the absence of time-delay, is PT-symmetric. The important parameters we control are the temporal separation of the lasers, the frequency detuning, and the coupling strength. The detuning is experimentally controlled by varying the lasers' temperatures, and intensity vs. detuning behavior are examined, specifically how the PT-transition and the period and amplitude of sideband intensity oscillations change with coupling and delay. Experiments are compared to analytic predictions and numerical results, and all are found to be in good agreement. Eigenvalues, eigenvectors, and exceptional points of the reduced Hamiltonian model are numerically and analytically investigated, specifically how nonzero delay affects existing exceptional points.
Voltage Controlled Non-Volatile Spin State and Conductance Switching of a Molecular Thin Film Heterostructure
(2021-05) Mosey, Aaron; Cheng, Ruihua; Joglekar, Yogesh; Decca, Ricardo; Vermuri, Gautum; Csathy, Gabor
Thermal constraints and the quantum limit will soon put a boundary on the scale of new micro and nano magnetoelectronic devices. This necessitates a push into the limits of harnessable natural phenomena to facilitate a post-Moore’s era of design. Requirements for thermodynamic stability at room temperature, fast (Ghz) switching, and low energy cost narrow the list of candidates. Here we show voltage controllable, room temperature, stable locking of the spin state, and the corresponding conductivity change, when molecular spin crossover thin films are deposited on a ferroelectric substrate. This opens the door to the creation of a non-volatile, room temperature, molecular multiferroic gated voltage controlled device.
Developing an approach to improve beta-phase properties in ferroelectric pvd-hfp thin films
(2020-05) Dale, Ashley S.; Cheng, Ruihua; Petrache, Horia; Wassall, Stephen
Improved fabrication of poly(vinylindenefluoride)-hexafluoropropylene (PVDF-HFP) thin films is of particular interest due to the high electric coercivity found in the beta-phase structure of the thin film. We show that it is possible to obtain high-quality, beta-phase dominant PVDF-HFP thin films using a direct approach to Langmuir-Blodgett deposition without the use of annealing or additives. To improve sample quality, an automated Langmuir-Blodgett thin film deposition system was developed; a custom dipping trough was fabricated, a sample dipping mechanism was designed and constructed, and the system was automated using custom LabVIEW software. Samples were fabricated in the form of ferroelectric capacitors on substrates of glass and silicon, and implement a unique step design with a bottom electrode of copper with an aluminum wetting layer and a top electrode of gold with an aluminum wetting layer. Samples were then characterized using a custom ferroelectric measurement program implemented in LabVIEW with a Keithley picoammeter/voltage supply to confirm electric coercivity properties. Further characterization using scanning electron microscopy and atomic force microscopy confirmed the improvement in thin film fabrication over previous methods.
Small Angle Scattering Of Large Protein Units Under Osmotic Stress
(2020-05) Palacio, Luis A.; Petrache, Horia I.; Cheng, Ruihua; Joglekar, Yogesh N.; Liu, Jing; Wassall, Stephen R.
Large protein molecules are abundant in biological cells but are very difficult to study in physiological conditions due to molecular disorder. For large proteins, most structural information is obtained in crystalline states which can be achieved in certain conditions at very low temperature. X-ray and neutron crystallography methods can then be used for determination of crystalline structures at atomic level. However, in solution at room or physiological temperatures such highly resolved descriptions cannot be obtained except in very few cases. Scattering methods that can be used to study this type of structures at room temperature include small-angle x-ray and neutron scattering. These methods are used here to study two distinct proteins that are both classified as glycoproteins, which are a large class of proteins with diverse biological functions. In this study, two specific plasma glycoproteins were used: Fibrinogen (340 kDa) and Alpha 1-Antitrypsin or A1AT (52 kDa). These proteins have been chosen based on the fact that they have a propensity to form very large molecular aggregates due to their tendency to polymerize. One goal of this project is to show that for such complex structures, a combination of scattering methods that include SAXS, SANS, and DLS can address important structural and interaction questions despite the fact that atomic resolution cannot be obtained as in crystallography. A1AT protein has been shown to have protective roles of lung cells against emphysema, while fibrinogen is a major factor in the blood clotting process. A systematic approach to study these proteins interactions with lipid membranes and other proteins, using contrast-matching small-angle neutron scattering (SANS), small angle x-ray scattering (SAXS) and dynamic light scattering (DLS), is presented here. A series of structural reference points for each protein in solution were determined by performing measurements under osmotic stress controlled by the addition of polyethylene glycol-1,500 MW (PEG 1500) in the samples. Osmotic pressure changes the free energy of the molecular mixture and has consequences on the structure and the interaction of molecular aggregates. In particular, the measured radius of gyration (Rg) for A1AT shows a sharp structural transition when the concentration of PEG 1500 is between 33 wt% and 36 wt%. Similarly, a significant structural change was observed for fibrinogen when the concentration of PEG 1500 was above 40 wt%. This analysis is applied to a study of A1AT interacting with lipid membranes and to a study of fibrinogen polymerization in the presence of the enzyme thrombin, which catalyzes the formation of blood clots. The experimental approach presented here and the applications to specific questions show that an appropriate combination of scattering methods can produce useful information on the behavior and the interactions of large protein systems in physiological conditions despite the lower resolution compared to crystallography.
Parity-Time Symmetry in Non-Hermitian Quantum Walks
(2019-12) Assogba Onanga, Franck; Joglekar, Yogesh; Decca, Ricardo; Vemuri, Gautam; Wassall, Stephen; Csathy, Gabor
Over the last two decades a new theory has been developed and intensively investigated in quantum physics. The theory stipulates that a non-Hermitian Hamiltonian can also represents a physical system as long as its energy spectra can be purely real in certain regime depending on the parameters of the Hamiltonian. It was demonstrated that the reality of the eigenenergy was conditioned by a certain kind of symmetry embedded in the actual non-Hermitian system. Indeed, such systems have a combined reflection (parity) symmetry (P) and time-reversal symmetry (T), PT-symmetry. The theory opens the door to new features particularly in open systems in which there could be gain and/or loss of particle or energy from and/or to the environment. A key property of the theory is the PT-symmetry breaking transition which occurs at the exceptional point (EP). The exceptional points are special degeneracies characterized by a coalescence of not only the eigenvalues but also of the corresponding eigenvectors of the system; and the coalescence happens when the gain-loss strength, a measure of the openness of the system, exceeds the intrinsic energy-scale of the system. In recent years, quantum walks with PT-symmetric non-unitary time evolution have been realized in systems with balanced gain and loss. These systems fall in two categories namely continuous time quantum walks (CTQW) that are characterized by a unitary or non-unitary time evolution Hamiltonian, and discrete-time quantum walks (DTQW) whose dynamic is described by a unitary or non-unitary time evolution operator consisting of a product of shift, coin, and gain-loss operations. In this thesis, we investigate the PT-symmetric phase of CTQW and DTQW in a variety of non-Hermitian lattice systems with both position-dependent and position independent, parity-symmetric tunneling functions in the presence of PT-symmetric impurities located at arbitrary parity-symmetric site on the lattice. Moreover, we explore the topological phase diagram and its novel features in non-Hermitian, homogeneous and non-homogeneous, PT-symmetric DTQW with closed and open boundary conditions. We conduct our study using analytical and numerical approaches that are directly and easily implementable in physical experiments. Among others, we found that, despite their non-unitary evolution, open systems governed by parity-time symmetric Hamiltonian support conserved quantities and that the PT-symmetry breaking threshold depends on the physical structure of the Hamiltonian and its underlying symmetries.
Optical refrigeration on CdSe/CdS quantum dots
(2019-12) Hua, Muchuan; Decca, Ricardo S.; Li, Tongcang; Cheng, Ruihua; Joglekar, Yogesh N.; Liu, Jing
Optical refrigeration in quantum dots was carried out in this research. Zinc-blende crystalline CdSe/CdS (core/shell structure) QDs with complete surface passivation were synthesized and been used as the cooling substance. Phonon-assisted up-conversion photoluminescence driven by sub-band gap laser excitation was utilized as the cooling mechanism in the QD samples. A net cooling efficiency was predicted by a semi-empirical model developed during the research, within a range of the laser excitation energy, even after taking into account possible parasitic heating processes. To observe the cooling effect, the experiment was carried out in a thermally isolated environment, which temperature was also monitored. By using an optical thermometry technique developed for this research, a maximum temperature drop around 0.68 K was observed in the experiment. This development paves the way to use QDs' cooling in new industrial and fundamental research approaches.
Parametric Cooling and Itinerant Ferromagnetism in a Degenerate Fermi Gas
(2018-12) de Melo, Leonardo F.; Cheng, Ruihua; Luo, Le; Greene, Chris; Joglekar, Yogesh; Petrache, Horia
Presented in this thesis is the construction of an apparatus to produce optically trapped lithium-6 atoms in the two lowest hyperfine states, the observation of cooling the trapped atoms by parametric excitation, and a study on the searching for itinerant ferromagnetism in a two-dimensional Fermi gas. In the parametric cooling experiment, a technique is developed to cool a cold atomic Fermi gas by parametrically driving atomic motions in a crossed-beam optical dipole trap. This method employs the anharmonicity of the optical dipole trap, in which the hotter atoms at the edge of the trap feel the anharmonic components of the trapping potential, while the colder atoms in the center of the trap feel the harmonic one. By modulating the trap depth with frequencies that are resonant with the anharmonic components, hotter atoms are selectively excited out of the trap while keeping the colder atoms in the trap, generating a cooling effect. An analytical study of itinerant ferromagnetism in a two-dimensional atomic Fermi gas is presented, based on the past experiments done with three-dimensional Fermi gases. Here, the formation of repulsive polarons in a strongly-interacting Fermi gas is used as an initial condition. Then the observation of itinerant ferromagnetism is realized by detection of ferromagnetic domains in the two-dimensional gas. Additionally, an experiment and simulation is performed on the effect of velocity-changing collisions on the absolute absorption of lithium-6 vapor in an argon buffer gas. The dependence of probe beam absorption is observed by variation of beam intensity and spatial evolution. The simulation of an effective three-level energy model with velocity-changing collisions determines a collision rate that agrees with transmission data collected.

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