Time periodicity from randomness in quantum systems

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.

arXiv comment5+5 pages; 3 figures

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• Embedding Quantum Many-Body Scars into Decoherence-Free Subspaces
• Quantum non-stationary phenomena of spin systems in collision models
• Powering an autonomous clock with quantum electromechanics
• Opening Krylov space to access all-time dynamics via dynamical symmetries
• Engineering Hierarchical Symmetries
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• Stability of emergent time periodicity in a few-body interacting system