Exponentially Accelerated Approach to Stationarity in Markovian Open Quantum Systems through the Mpemba Effect

F. C. and I. L. acknowledge support from the Wissenschaftler-Ruckkehrprogramm GSO/CZS of the Carl-Zeiss-Stiftung and the German Scholars Organization e.V., as well as through the Deutsche Forschungsgemeinsschaft (DFG, German Research Foundation) under Project No. 435696605. A. L. acknowledges support from the Spanish Ministerio de Ciencia, Innovacion y Universidades, and the Agencia Estatal de Investigacion through Grants No. MTM2017-84446-C2-2-R and No. PID2020-116567GB-C22.Ergodicity breaking and slow relaxation are intriguing aspects of nonequilibrium dynamics both in classical and 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 timescales 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 no longer excites 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 speeding-up in the convergence to stationarity in Dicke models, and how to avoid metastable regimes in an all-to-all interacting spin system.Wissenschaftler-Ruckkehrprogramm GSO/CZS of the Carl-Zeiss-StiftungGerman Scholars Organization e.V.German Research Foundation (DFG) 435696605Spanish Ministerio de Ciencia, Innovacion y UniversidadesAgencia Estatal de Investigacion MTM2017-84446-C2-2-R PID2020-116567GB-C2