A general interpretation of nonlinear connected time crystals: quantum self-sustaining combined with quantum synchronization

TL;DR

This paper presents a framework for understanding nonlinear quantum time crystals, emphasizing the role of quantum synchronization and phase correlations in sustaining oscillations, with a concrete example of van der Pol oscillators.

Contribution

It introduces a novel interpretation linking quantum synchronization with time-crystal behavior, simplifying the identification process in many-body systems.

Findings

Quantum synchronization enables continuous time crystals.

Dephasing suppresses time-crystal behavior, which can be mitigated by phase correlations.

Spontaneous oscillations confirmed in a synchronized array of van der Pol oscillators.

Abstract

Although classical nonlinear dynamics suggests that sufficiently strong nonlinearity can sustain oscillations, quantization of such model typically yields a time-independent steady state that respects time-translation symmetry and thus precludes time-crystal behavior. We identify dephasing as the primary mechanism enforcing this symmetry, which can be suppressed by intercomponent phase correlations. Consequently, a sufficient condition for realizing a continuous time crystal is a nonlinear quantum self-sustaining system exhibiting quantum synchronization among its constituents. As a concrete example, we demonstrate spontaneous oscillations in a synchronized array of van der Pol oscillators, corroborated by both semiclassical dynamics and the quantum Liouville spectrum. These results reduce the identification of time crystals in many-body systems to the evaluation of only two-body correlations and provide a framework for classifying uncorrelated time crystals as trivial.