Browsing by Subject "PT symmetry"

Now showing 1 - 5 of 5
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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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    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.
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    PT symmetry breaking in the presence of random, periodic, long-range hopping
    (SPIE, 2016-09) Harter, Andrew K.; Assogba Onanga, Franck; Joglekar, Yogesh N.; Department of Physics, School of Science
    Over the past five years, open systems with balanced gain and loss have been investigated for extraordinary properties that are not shared by their closed counterparts. Non-Hermitian, Parity-Time (PT ) symmetric Hamiltonians faithfully model such systems. Such a Hamiltonian typically consists of a reflection-symmetric, Hermitian, nearest-neighbor hopping profile and a PT-symmetric, non-Hermitian, gain and loss potential, and has a robust PT -symmetric phase. Here we investigate the robustness of this phase in the presence of long-range hopping disorder that is not PT-symmetric, but is periodic. We find that the PT-symmetric phase remains robust in the presence of such disorder, and characterize the configurations where that happens. Our results are found using a tight-binding model, and we validate our predictions through the beam-propagation method.
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    Theoretical and experimental characterization of non-Markovian anti-parity-time systems
    (Springer, 2023-10-20) Wilkey, Andrew; Suelzer, Joseph; Joglekar, Yogesh N.; Vemuri, Gautam; Physics, School of Science
    Open systems with anti-parity-time (APT) or PT symmetry exhibit a rich phenomenology absent in their Hermitian counterparts. To date all model systems and their diverse realizations across classical and quantum platforms have been local in time, i.e., Markovian. Here we propose a non-Markovian system with anti-PT-symmetry where a single time-delay encodes the retention of memory, and experimentally demonstrate its consequences with two time-delay coupled semiconductor lasers. A transcendental characteristic equation with infinitely many eigenvalue pairs sets our model apart. We show that a sequence of amplifying-to-decaying dominant mode transitions is induced by the time delay in our minimal model. The signatures of these transitions quantitatively match results obtained from four, coupled, nonlinear rate equations for laser dynamics, and are experimentally observed as constant-width sideband oscillations in the laser intensity profiles. Our work introduces a paradigmatic non-Hermitian system with memory, paves the way for its realization in classical systems, and may apply to time-delayed feedback-control for quantum systems.
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    Veiled symmetry of disordered Parity-Time lattices: protected PT-threshold and the fate of localization
    (Nature Publishing Group, 2018-01-08) Harter, Andrew K.; Assogba Onanga, Franck; Joglekar, Yogesh N.; Physics, School of Science
    Open, non-equilibrium systems with balanced gain and loss, known as parity-time ([Formula: see text])-symmetric systems, exhibit properties that are absent in closed, isolated systems. A key property is the [Formula: see text]-symmetry breaking transition, which occurs when the gain-loss strength, a measure of the openness of the system, exceeds the intrinsic energy-scale of the system. We analyze the fate of this transition in disordered lattices with non-Hermitian gain and loss potentials ±iγ at reflection-symmetric sites. Contrary to the popular belief, we show that the [Formula: see text]-symmetric phase is protected in the presence of a periodic disorder which leads to a positive [Formula: see text]-symmetry breaking threshold. We uncover a veiled symmetry of such disordered systems that is instrumental for the said protection, and show that this symmetry leads to new localization behavior across the [Formula: see text]-symmetry breaking transition. We elucidate the interplay between such localization and the [Formula: see text]-symmetry breaking phenomena in disordered [Formula: see text]-symmetric lattices, with Hermitian disorder or gain-loss disorder, and support our conclusions with a beampropagation- method analysis. Our theoretical predictions provide avenues for experimental realizations of -symmetric systems with engineered disorder.