Time Crystals in Open Systems

Andreu Riera-Campeny, Maria Moreno-Cardoner, Anna Sanpera

Time crystals are genuinely non-equilibrium quantum phases of matter that break time-translational symmetry. While in non-equilibrium closed systems time crystals have been experimentally realized, it remains an open question whether or not such a phase survives when systems are coupled to an environment. Although dissipation caused by the coupling to a bath may stabilize time crystals in some regimes, the introduction of incoherent noise may also destroy the time crystalline order. Therefore, the mechanisms that stabilize a time crystal in open and closed systems are not necessarily the same. Here, we propose a way to identify an open system time crystal based on a single object: the Floquet propagator. Armed with such a description we show time-crystalline behavior in an explicitly short-range interacting open system and demonstrate the crucial role of the nature of the decay processes.

Norman Y. Yao

Robert Mattes, Igor Lesanovsky, Federico Carollo

Time crystals are nonequilibrium many-body phases in which the state of the system dynamically approaches a limit cycle. While these phases have recently been the focus of intensive research, it is still far from clear whether they can host quantum correlations. In fact, mostly classical correlations have been observed so far, and time crystals appear to be effectively classical high-entropy phases. Here, we consider the nonequilibrium behavior of an open quantum light-matter system, realizable in current experiments, which maps to a paradigmatic time-crystal model after an adiabatic elimination of the light field. The system displays a bistable regime with coexistent time-crystal and stationary phases, terminating at a tricritical point from which a second-order phase transition line departs. While light and matter are uncorrelated in the stationary phase, the time-crystal phase features bipartite correlations of both quantum and classical nature. Our work unveils that time-crystal phases in collective open quantum systems can sustain quantum correlations, including entanglement, and are thus more than effectively classical many-body phases.

J. Zhang, Paul Hess, A. Kyprianidis +9 more

Yuechun Jiao, Weilun Jiang, Yu Long Zhang +5 more

Time crystals, as temporal analogs of space crystals, manifest as stable and periodic behavior that breaks time translation symmetry. In an open quantum system, many-body interaction subjected to dissipation allows one to develop the time crystalline order in an unprecedented way, as refer to dissipative time crystals. Here we report the observation of multiple time crystals in the continuously driven-dissipative and strongly interacting Rydberg thermal gases, in which continuous time crystals, sub-harmonic time crystals, and high-harmonic time crystals are observed in the same system by manipulating the Rydberg excitation. Our work provides new ways to explore the nonequilibrium phases of matter in open systems. Such time crystals with persistent oscillation rooted in emergent quantum correlations, may emerge as a ubiquitous tool in quantum metrology, for instance, continuous sensing and parameter estimation surpassing the standard quantum limit.

A. Kyprianidis, J. Zhang, Paul Hess +9 more