Discrete time crystals in the presence of non-Markovian dynamics

We study discrete time crystals (DTCs) in periodically driven quantum systems, in the presence of non-Markovian dissipation.In contrast to DTCs observed in earlier works in the presence of Markovian dynamics, using the open Dicke model in presence of Jaynes-Cummings-like dissipation, we show that non-Markovian regime can be highly beneficial for stabilizing DTCs over a wide range of parameter values.This may be attributed to periodically varying dissipation rates even at long times in the case of non-Markovian dynamics.Further the Markovian and non-Markovian regimes show sharp distinctions for intermediate strengths of the dissipator coefficient, with a time-independent steady-state in the Markovian regime being replaced by varied dynamical phases, including DTC order, in the non-Markovian regime.We also verify the robustness of the DTC phase in the non-Markovian regime by introducing errors both in the Hamiltonian as well as in the dissipation.Our study shows the possibility of using DTC as a probe for non-Markovian dynamics in periodically modulated open quantum systems, at long times.