Browsing by Subject "parity-time symmetry"

Now showing 1 - 5 of 5
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    Conserved quantities in non-hermitian systems via vectorization method
    (CTU, 2022-02-28) Agarwal, Kaustubh S.; Muldoon, Jacob; Joglekar, Yogesh N.; Physics, School of Science
    Open classical and quantum systems have attracted great interest in the past two decades. These include systems described by non-Hermitian Hamiltonians with parity-time (PT) symmetry that are best understood as systems with balanced, separated gain and loss. Here, we present an alternative way to characterize and derive conserved quantities, or intertwining operators, in such open systems. As a consequence, we also obtain non-Hermitian or Hermitian operators whose expectations values show single exponential time dependence. By using a simple example of a PT-symmetric dimer that arises in two distinct physical realizations, we demonstrate our procedure for static Hamiltonians and generalize it to time-periodic (Floquet) cases where intertwining operators are stroboscopically conserved. Inspired by the Lindblad density matrix equation, our approach provides a useful addition to the well-established methods for characterizing time-invariants in non-Hermitian systems.
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    Exceptional Points in a Non-Markovian Anti-Parity-Time Symmetric System
    (MDPI, 2023-12) Wilkey, Andrew; Joglekar, Yogesh N.; Vemuri, Gautam; Physics, School of Science
    By studying the eigenvalues and eigenvectors of a non-Markovian anti parity-time (APT) symmetric system, we investigate the possibility of exceptional points (EPs) that may arise within it. Our work is motivated by a recently studied APT-symmetric experimental configuration consisting of a pair of time-delay coupled semiconductor lasers (SCLs). In such a system, a single time-delay represents the memory. The time-delayed coupling makes the system’s effective Hamiltonian infinite-dimensional and leads to novel features in the corresponding eigenvalues and eigenvectors. In particular, we demonstrate analytically and numerically that unlike a typical PT-symmetric dimer with zero time-delay, which has one second-order EP, our time-delayed system has parameter regimes that give rise to either one, two, or zero second-order EPs and one third-order EP, and one can select these regimes though a judicious choice of the time-delay and coupling.
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    Non-hermitian dynamics in delay coupled semiconductor lasers
    (SPIE, 2019-08) Wilkey, Andrew; Suelzer, Joseph S.; Joglekar, Yogesh; Vemuri, Gautam; Physics, School of Science
    This paper describes our work on the realization of a non-hermitian Hamiltonian system in time-delay coupled semiconductor lasers consisting of two identical lasers, operated with a small frequency detuning between them, and bidirectionally coupled to each other through optical injection. The effective Hamiltonian for this system is non-hermitian, and, under some assumptions and conditions, reminiscent of two-site paritytime (PT) symmetric Hamiltonians, a topic that is under intense investigation. The dynamical response of the intensity of the lasers as a function of the detuning between them reveals characteristics of a PT symmetric system, and our emphasis is on the features that arise from the delayed coupling. Experimental measurements are in good agreement with numerical simulation of the nonlinear rate equation model that describes the coupled system.
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    PT-symmetry breaking in quantum spin chains with exceptional non-Hermiticities
    (APS, 2023) Muldoon, Jacob; Joglekar, Yogesh N.; Physics, School of Science
    Since the realization of quantum systems described by non-Hermitian Hamiltonians with parity-time () symmetry, interest in non-Hermitian, quantum many-body models has steadily grown. Most studies to date map to traditional quantum spin models with a non-Hermiticity that arises from making the model parameters complex or purely imaginary. Here we present a set of models with non-Hermiticity generated by splitting a Hermitian term into two Jordan-normal form parts, and the perturbations are confined to one or two sites. We present exact diagonalization results for a finite threshold in such models and provide an analytical approach for understanding the numerical results. Surprisingly, with non-Hermitian potentials confined to two or even a single site, the threshold seems insensitive to the size of the quantum spin chain. Our results provide a pathway to experimentally feasible non-Hermitian quantum spin chains where the confluence of many-body effects and non-Hermiticity effects can be observed.
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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.