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Ergodicity-breaking and slow relaxation are intriguing aspects ofnonequilibrium dynamics both in classical and in quantum settings. Thesephenomena are typically associated with phase transitions, e.g. the emergenceof metastable regimes near a first-order transition or scaling dynamics in thevicinity of critical points. Despite being of fundamental interest theassociated divergent time scales are a hindrance when trying to exploresteady-state properties. Here we show that the relaxation dynamics of Markovianopen quantum systems can be accelerated exponentially by devising an optimalunitary transformation that is applied to the quantum system immediately beforethe actual dynamics. This initial "rotation" is engineered in such a way thatthe state of the quantum system becomes orthogonal to the slowest decayingdynamical mode. We illustrate our idea -- which is inspired by the so-calledMpemba effect, i.e., water freezing faster when initially heated up -- byshowing how to achieve an exponential speed-up in the convergence tostationarity in Dicke models, and how to avoid metastable regimes in anall-to-all interacting spin system.

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