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

Carollo, Federico; Lasanta, Antonio; Lesanovsky, Igor

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 does not excite anymore 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. Introduction.-A strong focus of current research in many-body quantum physics is on understanding (nonequilibrium) phases of matter and transitions between them. Often associated with that are slow relaxation and divergent time-correlations [1-7], which typically signal the onset of critical behavior [8-13] or the appearance of metastable dynamical regimes [14, 15] near first order phase transitions. In certain instances, the concomitant very long relaxation time scales become impractical or even detrimental when a fast approach to stationarity is desired. This is certainly the case when one is interested in studying steady-state properties [16], or, for instance, when the stationary state encodes the result of some computation [17-19]. It may also find applications in the optimization of the output of quantum engines [20-23]. In physical terms, the characteristic time needed for an open dissipative quantum system to approach stationarity is given by the lifetime τ of the slowest decaying excitation mode. A random initial pure state |ψ [see Fig. 1(a)] is typically out-of-equilibrium and excites all dynamical decaying modes, including the slowest one. As such, it will ultimately converge to sta-tionarity in a time proportional to τ .

Citation

Carollo, F., Lasanta, A., & Lesanovsky, I. (2021). Exponentially accelerated approach to stationarity in Markovian open quantum systems through the Mpemba effect. Physical Review Letters, 127(6), Article 060401. https://doi.org/10.1103/PhysRevLett.127.060401

• Journal Article Type: Letter
• Acceptance Date: Jul 2, 2021
• Online Publication Date: Aug 2, 2021
• Publication Date: Aug 6, 2021
• Deposit Date: Jul 22, 2021
• Publicly Available Date: Aug 2, 2021
• Journal: Physical Review Letters
• Print ISSN: 0031-9007
• Electronic ISSN: 1079-7114
• Publisher: American Physical Society
• Peer Reviewed: Peer Reviewed
• Volume: 127
• Issue: 6
• Article Number: 060401
• DOI: https://doi.org/10.1103/PhysRevLett.127.060401
• Keywords: General Physics and Astronomy
• Public URL: https://nottingham-repository.worktribe.com/output/5813155
• Publisher URL: https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.127.060401