Quantum Mpemba effect in parity-time symmetric systems

Abstract: The quantum Mpemba effect (QMPE), an anomalous relaxation phenomenon, has been demonstrated in both closed and open Hermitian quantum systems. While prior studies have linked the QMPE to Liouvillian exceptional points--non-Hermitian features emerged at the Liouvillian level, it remains largely elusive whether the QMPE can occur in intrinsic non-Hermitian systems, where non-Hermiticity is inherent at the Hamiltonian level. Here, we unequivocally demonstrate the occurrence of QMPE in experimentally realizable parity-time-symmetric qubit systems immersed in a bosonic bath. Surprisingly, we find that exceptional points are neither sufficient nor necessary for the QMPE in this context, contrasting previous findings. Specifically, we show 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. Owing to the complete suppression of the slowest relaxation mode facilitated by parity-time symmetry, we attribute the observed QMPE to a cooperative effect of remaining relaxation modes. We obtain analytical expressions that delineate the parameter regimes supporting the QMPE. Our findings not only broaden the scope of the QMPE but also reveal its intricate interplay with non-Hermitian features beyond exceptional points.