Exponentially accelerated approach to stationarity in Markovian open quantum systems through the Mpemba effect

TL;DR

This paper introduces a method inspired by the Mpemba effect to exponentially accelerate the relaxation to stationarity in Markovian open quantum systems by applying an optimal initial unitary transformation.

Contribution

It presents a novel approach to speed up quantum system relaxation by pre-rotating states to orthogonalize them against slow modes, reducing convergence time exponentially.

Findings

Achieved exponential speed-up in Dicke models.

Avoided metastable regimes in spin systems.

Demonstrated effectiveness of optimal initial rotations.

Abstract

Ergodicity-breaking and slow relaxation are intriguing aspects of nonequilibrium dynamics both in classical and in quantum settings. These phenomena are typically associated with phase transitions, e.g. the emergence of metastable regimes near a first-order transition or scaling dynamics in the vicinity of critical points. Despite being of fundamental interest the associated divergent time scales are a hindrance when trying to explore steady-state properties. Here we show that the relaxation dynamics of Markovian open quantum systems can be accelerated exponentially by devising an optimal unitary transformation that is applied to the quantum system immediately before the actual dynamics. This initial "rotation" is engineered in such a way that the state of the quantum system becomes orthogonal to the slowest decaying dynamical mode. We illustrate our idea -- which is inspired by the so-called Mpemba effect, i.e., water freezing faster when initially heated up -- by showing how to achieve an exponential speed-up in the convergence to stationarity in Dicke models, and how to avoid metastable regimes in an all-to-all interacting spin system.