Metastable discrete time-crystal resonances in a dissipative central spin system

TL;DR

This paper investigates complex metastable oscillations, called time-crystal resonances, in a dissipative central spin system under periodic resets, revealing long-lived non-equilibrium dynamics and potential links to quantum synchronization.

Contribution

It introduces the concept of metastable time-crystal resonances in a simple dissipative quantum system and develops an effective theory for their long-lived dynamics.

Findings

Identification of metastable time-crystal resonances with long-lived oscillations

Development of an effective description within the metastable subspace

Long-time approach to a non-equilibrium stationary state

Abstract

We consider the non-equilibrium behavior of a central spin system where the central spin is periodically reset to its ground state. The quantum mechanical evolution under this effectively dissipative dynamics is described by a discrete-time quantum map. Despite its simplicity this problem shows surprisingly complex dynamical features. In particular, we identify several metastable time-crystal resonances. Here the system does not relax rapidly to a stationary state but undergoes long-lived oscillations with a period that is an integer multiple of the reset period. At these resonances the evolution becomes restricted to a low-dimensional state space within which the system undergoes a periodic motion. Generalizing the theory of metastability in open quantum systems, we develop an effective description for the evolution within this long-lived metastable subspace and show that in the long-time limit a non-equilibrium stationary state is approached. Our study links to timely questions concerning emergent collective behavior in the 'prethermal' stage of a dissipative quantum many-body evolution and may establish an intriguing link to the phenomenon of quantum synchronization.