Abstract We study the dynamics of correlations in a paradigmatic setup to observe PT -symmetric physics: a pair of coupled oscillators, one subject to a gain one to a loss. Starting from a coherent state, quantum correlations (QCs) are created, despite the system being driven only incoherently, and can survive indefinitely. Both total and QCs exhibit different scalings of their long-time behavior in the PT -broken/unbroken phase and at the exceptional point (EP). In particular, PT symmetry breaking is accompanied by non-zero stationary QCs. This is analytically shown and quantitatively explained in terms of entropy balance. The EP in particular stands out as the most classical configuration, as classical correlations diverge while QCs vanish.
A pair of coupled quantum harmonic oscillators, one subject to a gain one to a loss, is a paradigmatic setup to implement PT-symmetric, non-Hermitian Hamiltonians in that one such Hamiltonian governs the mean-field dynamics for equal gain and loss strengths. Through a full quantum description (so as to account for quantum noise) here is shown that when the system starts in any two-mode coherent state, including vacuum, there appear quantum correlations (QCs) without entanglement, as measured by the Gaussian discord. When the loss rate is above a threshold, once generated QCs no more decay. This occurs in a wide region of parameters, significantly larger than that where the full quantum dynamics is stable. For equal gain and loss rates, in particular, QCs decay in the exact phase (including the exceptional point) and are stable in the broken phase.
With their conceptual description of Parity-Time symmetry in 1998 [1], Bender and Boettcher inaugurated a new field of studies with fascinating implications on topology [2] and exceptional point dynamics [3], to name a few. Typically, PT-symmetric Hamiltonians exhibit real eigenvalues below a certain threshold, whereas above, the PT-symmetry is spontaneously broken as the eigenvalue spectrum becomes complex. Entirely passive configurations based solely on differential losses [7] allow the physics of PT symmetry to be carried over to a quantum-optical context [6] and explored therein [4]. Here we study the ways in which the degree of loss systematically impacts the characteristics of quantum correlations between interfering photons by analyzing the two-photon correlations in PT-symmetric directional couplers.
Abstract The dynamics of an open quantum system with balanced gain and loss is not described by a PT-symmetric Hamiltonian but rather by Lindblad operators. Nevertheless the phenomenon of PT-symmetry breaking and the impact of exceptional points can be observed in the Lindbladean dynamics. Here we briefly review the development of PT symmetry in quantum mechanics, and the characterisation of PT-symmetry breaking in open quantum systems in terms of the behaviour of the speed of evolution of the state.
In the past years, many efforts have been made to study various noteworthy phenomena in both parity-time
(PT) and anti-parity-time
(APT) symmetric systems. However, entanglement dynamics in
APT-symmetric systems has not previously been investigated in both theory and experiments. Here, we investigate the entanglement evolution of two qubits in an
APT-symmetric system. In the
APT-symmetric unbroken regime, our theoretical simulations demonstrate the periodic oscillations of entanglement when each qubit evolves identically, while the nonperiodic oscillations of entanglement when each qubit evolves differently. In particular, when each qubit evolves near the exceptional point in the
APT-symmetric unbroken regime, there exist entanglement sudden vanishing and revival. Moreover, our simulations demonstrate rapid decay and delayed death of entanglement provided one qubit evolves in the
APT-symmetric broken regime. In this work, we also perform an experiment with a linear optical setup. The experimental results agree well with our theoretical simulation results. Our findings reveal novel phenomena of entanglement evolution in the
APT-symmetric system and opens a new direction for future studies on the dynamics of quantum entanglement in multiqubit
APT-symmetric systems or other non-Hermitian quantum systems.