Time periodicity from randomness in quantum systems

TL;DR

This paper demonstrates how spontaneous periodicity can emerge in open quantum systems through random interactions, with conditions ensuring oscillatory states, supported by spin model examples relevant for quantum simulation.

Contribution

It introduces dynamical symmetry conditions for oscillations in quantum systems with random interactions, advancing understanding of quantum self-oscillation without semi-classical limits.

Findings

Oscillatory long-time states can arise in open quantum systems with random couplings.

Dynamical symmetry conditions guarantee periodic behavior.

Spin models illustrate the theoretical results, feasible for quantum simulators.

Abstract

Many complex systems can spontaneously oscillate under non-periodic forcing. Such self-oscillators are commonplace in biological and technological assemblies where temporal periodicity is needed, such as the beating of a human heart or the vibration of a cello string. While self-oscillation is well understood in classical non-linear systems and their quantized counterparts, the spontaneous emergence of periodicity in quantum systems without a semi-classical limit is more elusive. Here, we show that this behavior can emerge within the repeated-interaction description of open quantum systems. Specifically, we consider a many-body quantum system that undergoes dissipation due to sequential coupling with auxiliary systems at random times. We develop dynamical symmetry conditions that guarantee an oscillatory long-time state in this setting. Our rigorous results are illustrated with specific spin models, which could be implemented in trapped-ion quantum simulators.