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arXiv:1811.05604 · Physical Review A

Quantum Zeno effect and nonclassicality in a PT -symmetric system of coupled cavities

Javid Naikoo, Kishore Thapliyal, Subhashish Banerjee, Anirban Pathak

Published Feb 11, 2019• 31 citations
arXivHTMLPDF

Abstract

The interplay between the nonclassical features and the parity-time ($\mathcal{PT}$) symmetry (or its breaking) is studied here by considering a $\mathcal{PT}$-symmetric system consisting of two cavities with gain and loss. The conditions for $\mathcal{PT}$ invariance are obtained for this system. The behavior of the average photon number corresponding to the gain and loss modes for different initial states (e.g., vacuum, NOON, coherent, and thermal states) has also been obtained. With the help of the number operators, quantum Zeno and anti-Zeno effects are studied, and the observed behavior is compared in $\mathcal{PT}$-symmetric (PTS) and $\mathcal{PT}$-symmetry-broken (PTSB) regimes. It has been observed that the relative phase of the input coherent fields plays a key role in the occurrence of these effects. Further, some nonclassicality features are witnessed using criteria based on the number operator(s). Specifically, intermodal antibunching, sum, and difference squeezing are investigated for specific input states. It is found that the various nonclassical features, including the observed quantum Zeno and anti-Zeno effects, are suppressed when one goes from the PTS to PTSB regime. In other words, the dominance of the loss or gain rate in the field modes over the coupling strength between them diminishes the nonclassical features of the system.

DOI
10.1103/physreva.99.023820

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The interplay between the nonclassical features and the parity-time (PT\mathcal{PT}PT) symmetry (or its breaking) is studied here by considering a PT\mathcal{PT}PT-symmetric system consisting of two cavities with gain and loss. The conditions for PT\mathcal{PT}PT invariance are obtained for this system. The behavior of the average photon number corresponding to the gain and loss modes for different initial states (e.g., vacuum, NOON, coherent, and thermal states) has also been obtained. With the help of the number operators, quantum Zeno and anti-Zeno effects are studied, and the observed behavior is compared in PT\mathcal{PT}PT-symmetric (PTS) and PT\mathcal{PT}PT-symmetry-broken (PTSB) regimes. It has been observed that the relative phase of the input coherent fields plays a key role in the occurrence of these effects. Further, some nonclassicality features are witnessed using criteria based on the number operator(s). Specifically, intermodal antibunching, sum, and difference squeezing are investigated for specific input states. It is found that the various nonclassical features, including the observed quantum Zeno and anti-Zeno effects, are suppressed when one goes from the PTS to PTSB regime. In other words, the dominance of the loss or gain rate in the field modes over the coupling strength between them diminishes the nonclassical features of the system.
A three-level atom in $\mathrm{\ensuremath{\Lambda}}$ configuration is reduced to an effective two-level system, under appropriate conditions, and its PT\mathcal{PT}PT symmetric properties are investigated. This effective qubit system, when subjected to a beam-splitter type of interaction, provides the scope of directly (indirectly) probing the nonclassical properties of the output (input) state. Here, we study nonclassical properties of the output state by using some well-known measures of nonclassical correlations like the measurement-induced disturbance, concurrence, and negativity. The nonclassical features are found to enhance in the PT\mathcal{PT}PT symmetric (PTS) phase compared to the PT\mathcal{PT}PT symmetry broken (PTB) phase. Further, the output ports of the beam splitter are subjected to different quantum noise channels, both non-Markovian, e.g., random telegraph noise as well as Markovian, e.g., phase damping and amplitude damping noise. The application of noise channels is found to decrease the degree of nonclassicality, though continuing to exhibit distinct behavior in PTS and PTB phases, with the dominant behavior appearing in the former case. Further, the results are compared with the case when dynamics is governed by a Hermitian Hamiltonian. This allows one to demarcate the contributions to nonclassicality from different types of dynamics.
Abstract We experimentally study quantum Zeno effects in a parity-time (PT) symmetric cold atom gas periodically coupled to a reservoir. Based on the state-of-the-art control of inter-site couplings of atoms in a momentum lattice, we implement a synthetic two-level system with passive PT symmetry over two lattice sites, where an effective dissipation is introduced through repeated couplings to the rest of the lattice. Quantum Zeno (anti-Zeno) effects manifest in our experiment as the overall dissipation of the two-level system becoming suppressed (enhanced) with increasing coupling intensity or frequency. We demonstrate that quantum Zeno regimes exist in the broken PT symmetry phase, and are bounded by exceptional points separating the PT symmetric and PT broken phases, as well as by a discrete set of critical coupling frequencies. Our experiment establishes the connection between PT-symmetry-breaking transitions and quantum Zeno effects, and is extendable to higher dimensions or to interacting regimes, thanks to the flexible control with atoms in a momentum lattice.
The decay of an unstable quantum state can be inhibited or enhanced by tailored measurements, known as quantum Zeno effect (QZE) or anti Zeno effect (QAZE). QZE(QAZE) has been intensively explored in terms of the cases of various system-environment couplings, where the time evolution can be affected either by the projective measurements, or through the dissipative couplings to the environment. A general relation between QZE(QAZE) and the dissipation, for arbitrary dissipation strength and periodicity, is yet to be developed. In this paper, we show a framework to unify the QZE(QAZE) and the parity-time (PT\mathcal{PT}PT) symmetry breaking transition, where the pure dissipative Hamiltonian is mapped onto a PT\mathcal{PT}PT symmetric non-Hermitian Hamiltonian. This method uses the PT\mathcal{PT}PT symmetry transitions to distinguish QZE and QAZE, and can be applied to analyze the crossover behavior between these two effects. Using a heuristic example of a two-level system which is coupled to environment by periodical dissipation, we show the relation diagram between the QZE(QAZE) and the PT\mathcal{PT}PT symmetry breaking transition, in which the QZE appears at an exceptional point that separates the PT\mathcal{PT}PT symmetric (PTS) phase and the PT\mathcal{PT}PT symmetry broken (PTSB) phase, and ends at the resonance point of the maximum PT\mathcal{PT}PT symmetry breaking; after that, QAZE exists at the rest of the PTSB phase and remains in the next PTS phase. This interesting finding reveals a hidden relation between the QZE--QAZE and PTS-PTSB phases in a non-Hermitian quantum system.
A two-mode optical parity-time (PT) symmetric system, with gain and damping, described by a quantum quadratic Hamiltonian with additional small Kerr-like nonlinear terms, is analyzed from the point of view of nonclassical-light generation. Two kinds of stationary states with different types of (in)stability are revealed. Properties of one of these are related to the presence of semiclassical exceptional points, i.e., exotic degeneracies of the non-Hermitian Hamiltonian describing the studied system without quantum jumps. The evolution of the logarithmic negativity, principal squeezing variances, and sub-shot-noise photon-number correlations, considered as entanglement and non-classicality quantifiers, is analyzed in the approximation of linear-operator corrections to the classical solution. Suitable conditions for nonclassical-light generation are identified in the oscillatory regime, especially at and around exceptional points that considerably enhance the nonlinear interaction and, thus, the non-classicality of the generated light. The role of quantum fluctuations, inevitably accompanying attenuation and amplification in the evolution of quantum states, is elucidated. The evolution of the system is analyzed for different initial conditions.
A two-mode optical parity-time (PT\mathcal{PT}PT) symmetric system, with gain and damping, described by a quantum quadratic Hamiltonian with additional small Kerr-like nonlinear terms, is analyzed from the point of view of nonclassical-light generation. Two kinds of stationary states with different types of (in)stability are revealed. Properties of one of these are related to the presence of semiclassical exceptional points, i.e., exotic degeneracies of the non-Hermitian Hamiltonian describing the studied system without quantum jumps. The evolution of the logarithmic negativity, principal squeezing variances, and sub-shot-noise photon-number correlations, considered as entanglement and nonclassicality quantifiers, is analyzed in the approximation of linear-operator corrections to the classical solution. Suitable conditions for nonclassical-light generation are identified in the oscillatory regime, especially at and around exceptional points that considerably enhance the nonlinear interaction and, thus, the nonclassicality of the generated light. The role of quantum fluctuations, inevitably accompanying attenuation and amplification in the evolution of quantum states, is elucidated. The evolution of the system is analyzed for different initial conditions.
The quantum Zeno and anti-Zeno effects describe how frequent measurements can either suppress or accelerate quantum dynamics. While extensively studied in various platforms, their manifestation in dark-state dynamics remains largely unexplored. Here we investigate the stability of dark states in a cavity quantum electrodynamics (QED) system consisting of two atoms coupled to a single-mode cavity, subject to thermal dephasing that models continuous quantum non-demolition monitoring. Using the Tavis--Cummings model within a Lindblad master equation framework, we perform numerical simulations to investigate how measurement-induced dephasing affects dark-state retention and stabilization time. Through systematic numerical scans, we identify distinct parameter regimes corresponding to Zeno and anti-Zeno behavior: at low dephasing intensities, increasing the measurement strength accelerates the loss of dark-state coherence (anti-Zeno regime), while at higher intensities, it slows down the dynamics and partially recovers dark-state weight (Zeno regime). The transition between these regimes is controlled by the dephasing rates, the cavity photon exchange, and the asymmetry in atom--field couplings. We show that even under strong dephasing, a finite dark-state component persists, demonstrating remarkable robustness. Our results provide insights into the interplay between measurement back-action and decoherence in open quantum systems, with implications for quantum control and information storage.