Browsing by Author "Assogba Onanga, Franck"

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    Conserved quantities in parity-time symmetric systems
    (APS, 2020) Bian, Zhihao; Xiao, Lei; Wang, Kunkun; Zhan, Xiang; Assogba Onanga, Franck; Ruzicka, Frantisek; Yi, Wei; Joglekar, Yogesh N.; Xue, Peng; Physics, School of Science
    Conserved quantities such as energy or the electric charge of a closed system, or the Runge-Lenz vector in Kepler dynamics, are determined by its global, local, or accidental symmetries. They were instrumental in advances such as the prediction of neutrinos in the (inverse) beta decay process and the development of self-consistent approximate methods for isolated or thermal many-body systems. In contrast, little is known about conservation laws and their consequences in open systems. Recently, a special class of these systems, called parity-time (PT) symmetric systems, has been intensely explored for their remarkable properties that are absent in their closed counterparts. A complete characterization and observation of conserved quantities in these systems and their consequences is still lacking. Here, we present a complete set of conserved observables for a broad class of PT-symmetric Hamiltonians and experimentally demonstrate their properties using a single-photon linear optical circuit. By simulating the dynamics of a four-site system across a fourth-order exceptional point, we measure its four conserved quantities and demonstrate their consequences. Our results spell out nonlocal conservation laws in nonunitary dynamics and provide key elements that will underpin the self-consistent analyses of non-Hermitian quantum many-body systems that are forthcoming.
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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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    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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    Quantum information dynamics in a high-dimensional parity-time-symmetric system
    (APS, 2020-09) Bian, Zhihao; Xiao, Lei; Wang, Kunkun; Assogba Onanga, Franck; Ruzicka, Frantisek; Yi, Wei; Joglekar, Yogesh N.; Xue, Peng; Physics, School of Science
    Non-Hermitian systems with parity-time (PT) symmetry give rise to exceptional points (EPs) with exceptional properties that arise due to the coalescence of eigenvectors. Such systems have been extensively explored in the classical domain, where second- or higher-order EPs have been proposed or realized. In contrast, quantum information studies of PT-symmetric systems have been confined to systems with a two-dimensional Hilbert space. Here, by using a single-photon interferometry setup, we simulate the quantum dynamics of a four-dimensional PT-symmetric system across a fourth-order exceptional point. By tracking the coherent, nonunitary evolution of the density matrix of the system in PT-symmetry unbroken and broken regions, we observe the entropy dynamics for both the entire system, and the gain and loss subsystems. Our setup is scalable to the higher-dimensional PT-symmetric systems, and our results point towards the rich dynamics and critical properties.
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    Time-invariant PT product and phase locking in PT -symmetric lattice models
    (APS, 2018-01) Joglekar, Yogesh N.; Assogba Onanga, Franck; Harter, Andrew K.; Physics, School of Science
    Over the past decade, non-Hermitian, PT -symmetric Hamiltonians have been investigated as candidates for both a fundamental, unitary, quantum theory and open systems with a nonunitary time evolution. In this paper, we investigate the implications of the former approach in the context of the latter. Motivated by the invariance of the PT (inner) product under time evolution, we discuss the dynamics of wave-function phases in a wide range of PT -symmetric lattice models. In particular, we numerically show that, starting with a random initial state, a universal, gain-site location dependent locking between wave-function phases at adjacent sites occurs in the PT -symmetry-broken region. Our results pave the way towards understanding the physically observable implications of time invariants in the nonunitary dynamics produced by PT -symmetric Hamiltonians.
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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.