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Browsing by Author "Joglekar, Yogesh N."
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Item 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.Item BREAKING OF SYMMETRY IN A PT-SYMMETRIC OPEN CHAIN(Office of the Vice Chancellor for Research, 2012-04-13) Barnett, Jacob L.; Joglekar, Yogesh N.The study of electromagnetic waves in engineering optical materials presents opportunities to manipulate light transmission through various optical media such as fiber optic cables. Recent experiments in this field have explored materials that have balanced gain and absorption that occur at different locations. We can model such a system as a chain with nearest neighbor hopping, and balanced, parity and time reversal symmetric (PT-symmetric) impurities, and it is represented by a non-Hermitian Hamiltonian matrix. The emergence of complex energy eigenvalues for such a matrix corresponds to the PT-symmetry breaking. We numerically and analytically investigate the eigenvalues of such a non-Hermitian Hamiltonian for an open chain with N sites. We find that the critical impurity strength, when the PT-symmetry breaks, is determined by the hopping amplitude between the impurities t_b, and hopping amplitude outside the impurities t_o in a non-trivial way. As a consequence, we show that the PT-breaking in such an open chain can be dramatically tuned by changing the hopping amplitude. Our results suggest that small changes in such systems, created in optical waveguides, can lead to significant changes for wave propagation through them (Joglekar, Y. N.,& Barnett, J. L., (2011). Origin of maximal symmetry breaking in even PT-symmetric lattices, Physical Review A, 84, 024103.)Item Classical Rabi Oscillations Induced By Unbalanced Dissipation On A Nonlinear Dimer(Elsevier, 2023-06) Humire, Fernando R.; Zárate, Yair D.; Joglekar, Yogesh N.; García-Ñustes, Mónica A.; Physics, School of ScienceClassical Rabi oscillations (ROs) are a signature feature of an unbroken parity-time (PT)-symmetry in conservative systems. Notwithstanding, they do not persist in systems with intrinsic dissipation from the surroundings. Here, we report permanent ROs in a parametrically driven and dissipative nonlinear dimer in a region of parameters where the conservative system exhibits broken PT-symmetry. We show that the mechanism for robust ROs lies in a suitable combination of typical gain/loss (PT-symmetry) configuration with nonlinearity and dissipation. This study presents a route to generate and control robust ROs in out-of-equilibrium systems in future experiments.Item Conserved quantities in non-hermitian systems via vectorization method(CTU, 2022-02-28) Agarwal, Kaustubh S.; Muldoon, Jacob; Joglekar, Yogesh N.; Physics, School of ScienceOpen 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.Item 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 ScienceConserved 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.Item Conserved quantities, exceptional points, and antilinear symmetries in non-Hermitian systems(IOP, 2021) Ruzicka, Frantisek; Agarwal, Kaustubh S.; Joglekar, Yogesh N.; Physics, School of ScienceOver 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, semiclassical models with mode selective losses, and minimal quantum systems, and the meteoric research on them has mainly focused on the wide range of novel functionalities they demonstrate. Here, we address the following questions: Does anything remain constant in the dynamics of such open systems? What are the consequences of such conserved quantities? Through spectral-decomposition method and explicit, recursive procedure, we obtain all conserved observables for general -symmetric systems. We then generalize the analysis to Hamiltonians with other antilinear symmetries, and discuss the consequences of conservation laws for open systems. We illustrate our findings with several physically motivated examples.Item Decoherence-Induced Exceptional Points in a Dissipative Superconducting Qubit(APS, 2022-03-17) Chen, Weijian; Abbasi, Maryam; Ha, Byung; Erdamar, Serra; Joglekar, Yogesh N.; Murch, Kater W.; Physics, School of ScienceOpen quantum systems interacting with an environment exhibit dynamics described by the combination of dissipation and coherent Hamiltonian evolution. Taken together, these effects are captured by a Liouvillian superoperator. The degeneracies of the (generically non-Hermitian) Liouvillian are exceptional points, which are associated with critical dynamics as the system approaches steady state. We use a superconducting transmon circuit coupled to an engineered environment to observe two different types of Liouvillian exceptional points that arise either from the interplay of energy loss and decoherence or purely due to decoherence. By dynamically tuning the Liouvillian superoperators in real time we observe a non-Hermiticity-induced chiral state transfer. Our study motivates a new look at open quantum system dynamics from the vantage of Liouvillian exceptional points, enabling applications of non-Hermitian dynamics in the understanding and control of open quantum systems.Item Emergent PT symmetry in a double-quantum-dot circuit QED setup(APS, 2020-10) Purkayastha, Archak; Kulkarni, Manas; Joglekar, Yogesh N.; Physics, School of ScienceOpen classical and quantum systems with effective parity-time ( PT ) symmetry, over the past five years, have shown tremendous promise for advances in lasers, sensing, and nonreciprocal devices. And yet, how such effective PT -symmetric non-Hermitian models emerge out of Hermitian quantum mechanics is not well understood. Here, starting from a fully Hermitian microscopic Hamiltonian description, we show that a non-Hermitian Hamiltonian emerges naturally in a double-quantum-dot (DQD) circuit-QED setup, which can be controllably tuned to the PT -symmetric point. This effective Hamiltonian governs the dynamics of two coupled circuit-QED cavities with a voltage-biased DQD in one of them. Our analysis also reveals the effect of quantum fluctuations on the PT -symmetric system. The PT transition is, then, observed both in the dynamics of cavity observables as well as via an input-output experiment. As a simple application of the PT transition in this setup, we show that loss-induced enhancement of amplification and lasing can be observed in the coupled cavities. By comparing our results with two conventional local Lindblad equations, we demonstrate the utility and limitations of the latter. Our results pave the way for an on-chip realization of a potentially scalable non-Hermitian system with a gain medium in the quantum regime, as well as its potential applications for quantum technology.Item Exactly solvable PT -symmetric models in two dimensions(IOP, 2015-11) Agarwal, Kaustubh S.; Pathak, Rajeev K.; Joglekar, Yogesh N.; Department of Physics, School of ScienceNon-Hermitian, $\mathcal{PT}$ -symmetric Hamiltonians, experimentally realized in optical systems, accurately model the properties of open, bosonic systems with balanced, spatially separated gain and loss. We present a family of exactly solvable, two-dimensional, $\mathcal{PT}$ potentials for a non-relativistic particle confined in a circular geometry. We show that the $\mathcal{PT}$ -symmetry threshold can be tuned by introducing a second gain-loss potential or its Hermitian counterpart. Our results explicitly demonstrate that $\mathcal{PT}$ breaking in two dimensions has a rich phase diagram, with multiple re-entrant $\mathcal{PT}$ -symmetric phases.Item Exceptional Points in a Non-Markovian Anti-Parity-Time Symmetric System(MDPI, 2023-12) Wilkey, Andrew; Joglekar, Yogesh N.; Vemuri, Gautam; Physics, School of ScienceBy 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.