Browsing by Author "Csathy, Gabor"

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    An investigation of parity and time-reversal symmetry breaking in tight-binding lattices
    (2014) Scott, Derek Douglas; Joglekar, Yogesh; Decca, Ricardo; Petrache, Horia; Tarasov, Vitaly; Csathy, Gabor
    More than a decade ago, it was shown that non-Hermitian Hamiltonians with combined parity (P) and time-reversal (T ) symmetry exhibit real eigenvalues over a range of parameters. Since then, the field of PT symmetry has seen rapid progress on both the theoretical and experimental fronts. These effective Hamiltonians are excellent candidates for describing open quantum systems with balanced gain and loss. Nature seems to be replete with examples of PT -symmetric systems; in fact, recent experimental investigations have observed the effects of PT symmetry breaking in systems as diverse as coupled mechanical pendula, coupled optical waveguides, and coupled electrical circuits. Recently, PT -symmetric Hamiltonians for tight-binding lattice models have been extensively investigated. Lattice models, in general, have been widely used in physics due to their analytical and numerical tractability. Perhaps one of the best systems for experimentally observing the effects of PT symmetry breaking in a one-dimensional lattice with tunable hopping is an array of evanescently-coupled optical waveguides. The tunneling between adjacent waveguides is tuned by adjusting the width of the barrier between them, and the imaginary part of the local refractive index provides the loss or gain in the respective waveguide. Calculating the time evolution of a wave packet on a lattice is relatively straightforward in the tight-binding model, allowing us to make predictions about the behavior of light propagating down an array of PT -symmetric waveguides. In this thesis, I investigate the the strength of the PT -symmetric phase (the region over which the eigenvalues are purely real) in lattices with a variety of PT - symmetric potentials. In Chapter 1, I begin with a brief review of the postulates of quantum mechanics, followed by an outline of the fundamental principles of PT - symmetric systems. Chapter 2 focuses on one-dimensional uniform lattices with a pair of PT -symmetric impurities in the case of open boundary conditions. I find that the PT phase is algebraically fragile except in the case of closest impurities, where the PT phase remains nonzero. In Chapter 3, I examine the case of periodic boundary conditions in uniform lattices, finding that the PT phase is not only nonzero, but also independent of the impurity spacing on the lattice. In addition, I explore the time evolution of a single-particle wave packet initially localized at a site. I find that in the case of periodic boundary conditions, the wave packet undergoes a preferential clockwise or counterclockwise motion around the ring. This behavior is quantified by a discrete momentum operator which assumes a maximum value at the PT -symmetry- breaking threshold. In Chapter 4, I investigate nonuniform lattices where the parity-symmetric hop- ping between neighboring sites can be tuned. I find that the PT phase remains strong in the case of closest impurities and fragile elsewhere. Chapter 5 explores the effects of the competition between localized and extended PT potentials on a lattice. I show that when the short-range impurities are maximally separated on the lattice, the PT phase is strengthened by adding short-range loss in the broad-loss region. Consequently, I predict that a broken PT symmetry can be restored by increasing the strength of the short-range impurities. Lastly, Chapter 6 summarizes my salient results and discusses areas which can be further developed in future research.
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    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.
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    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.