Theory for dissipative time crystals in coupled parametric oscillators

TL;DR

This paper introduces a classical model of coupled parametric oscillators to explore discrete time crystals, demonstrating their robustness through numerical and theoretical analyses relevant to quantum and classical systems.

Contribution

It proposes a classical oscillator system as a testbed for understanding dissipative time crystals, bridging classical and quantum perspectives with novel theoretical and numerical insights.

Findings

Existence of time crystal phase in the oscillator system

Robustness of the phase under symmetry-breaking dynamics

Relevance to quantum dissipative systems

Abstract

Discrete time crystals are novel phases of matter that break the discrete time translational symmetry of a periodically driven system. In this work, we propose a classical system of weakly-nonlinear parametrically-driven coupled oscillators as a testbed to understand these phases. Such a system of parametric oscillators can be used to model period-doubling instabilities of Josephson junction arrays as well as semiconductor lasers. To show that this instability leads to a discrete time crystal we first show that a certain limit of the system is close to Langevin dynamics in a symmetry breaking potential. We numerically show that this phase exists even in the presence of Ising symmetry breaking using a Glauber dynamics approximation. We then use a field theoretic argument to show that these results are robust to other approximations including the semiclassical limit when applied to dissipative quantum systems.