Quantum Mpemba effect in parity-time symmetric systems

TL;DR

This paper demonstrates the quantum Mpemba effect in parity-time symmetric qubit systems, revealing its persistence across various regimes and its independence from exceptional points, thus broadening understanding of non-Hermitian quantum dynamics.

Contribution

It provides the first clear demonstration of QMPE in intrinsic non-Hermitian systems and develops an analytical framework to understand its parameter dependence.

Findings

QMPE occurs in PT-symmetric qubit systems immersed in a bosonic bath.

QMPE persists across a wide parameter regime, independent of exceptional points.

QMPE is robust against increasing qubit number and dephasing effects.

Abstract

The quantum Mpemba effect (QMPE), an anomalous relaxation phenomenon, has been demonstrated in both closed and open Hermitian quantum systems. While some studies have linked the QMPE to Liouvillian exceptional points--non-Hermitian features emerged at the Liouvillian level--in open Hermitian quantum systems, it remains largely unexplored whether the QMPE can occur in intrinsic non-Hermitian systems, where non-Hermiticity is inherent at the Hamiltonian level. Here, we demonstrate unequivocally the occurrence of QMPE in experimentally realizable parity-time-symmetric qubit systems immersed in a bosonic bath. Using established quantifiers for QMPE, we show numerically that the QMPE persists across parameter regimes both near and far from Hamiltonian and Liouvillian exceptional points, but disappears entirely when Hermitian Hamiltonian is restored. Interestingly, neither Hamiltonian nor Liouvillian exceptional points demarcate the boundaries of the QMPE regime. To complement numerical results, we develop an analytical description based on a long-time approximation of the relaxation dynamics of quantifiers. This approach allows us to decipher the number of intersections between two dynamical trajectories of quantifier starting from two initial conditions in the validity regime of the long-time approximation, thereby providing additional information that delineate the parameter regimes supporting the genuine QMPE. We further demonstrate the robustness of QMPE against increasing the number of qubits and dephasing effect. Our findings not only broaden the scope of the QMPE but also suggest its intricate interplay with non-Hermitian features beyond exceptional points.