Theory for dissipative time crystals in coupled parametric oscillators
arXiv:2306.13652 · doi:10.1103/PhysRevLett.133.266601
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.
10 pages, 3 figures
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