Driven-Dissipative Time Crystalline Phases in a Two-Mode Bosonic System with Kerr Nonlinearity

Abstract

For the driven-dissipative system of two coupled bosonic modes in a nonlinear cavity resonator, we demonstrate a sequence of phase transitions from a trivial steady state to two distinct dissipative time crystalline phases. These effects are already anticipated at the level of the semiclassical analysis of the Lindblad equation using the theory of bifurcations and are further supported by the full quantum treatment. The system is predicted to exhibit different dynamical phases characterized by an oscillating nonequilibrium steady state with nontrivial periodicity, which is a hallmark of time crystals. We expect that these phases can be directly probed in various cavity QED experiments.

Quantifying spatio-temporal patterns in classical and quantum systems out of equilibrium

“…As it was shown in the previous works [40][41][42] DTC is formed as a result of breaking discrete time translation symmetry in a Floquet system with time-periodic Hamiltonian and retaining memory of the initial state indefinitely. Experimentally, it can be realized in systems of superconducting qubits 25,26,44 , but other platforms, for instance quantum-optical systems 43 are also promising candidates for observing this non-trivial state. The main signature of DTC, the spatio-temporal order can be detected and probed with the combination of temporal autocorrelators and qubit-qubit spatial correlation functions.…”