Session C22: Floquet Time Crystals

Floquet MBL phases in theory and experiment

Recent work suggests that a sharp definition of `phase of matter' can be given for some quantum systems out of equilibrium---first for many-body localized systems with time independent Hamiltonians and more recently for periodically driven or Floquet localized systems. We present a new family of driven Floquet phases which show non-trivial long time behavior in their local observables at late times, and comment on the results of recent experiments.   

Floquet Time Crystals

Periodically driven (Floquet) systems provide a setting to realize entirely new non-equilbrium phases of matter without stationary analogs. A unifying way to understand such phases is in terms of symmetries; Floquet phases of matter have a discrete time-translation symmetry which can protect new dynamical phases of matter. In this talk, we characterize a dramatic example of such a phase: the ``Floquet time crystals'', in which the discrete time-translation symmetry is spontaneously broken and local observables oscillate at some fraction of the drive frequency. We discuss two scenarios by which Floquet time crystals can be stabilized: many-body localization and pre-thermalization. In the latter case, Floquet ordering persists until a thermalization time that is exponentially large in a small paramater. We show that pre-thermalization also allows other Floquet phases of matter to be stabilized, including some which have too much symmetry to be compatible with many-body-localization.   

Realization of discrete time crystals in a spin chain of trapped ions

Linear arrays of trapped atomic ions are a unique experimental platform for studying emergent phenomenon in many-body quantum physics. Using laser light to drive collective ion motion, we generate long-range interactions between trapped ion spins and realize models of frustrated quantum magnetism. Local control and individual spin resolution allow us to study such models in ways not possible using condensed matter experiments. I will discuss recent results where our trapped ions were used to study universal properties when these spin models are subjected to Floquet drives. Our system responds with sub-harmonic oscillations which are stabilized by the many-body interactions, which are clear signatures of a state known as a discrete time crystal.   

Rigidity and Criticality in Discrete Time Crystals

Despite being forbidden in equilibrium, spontaneous breaking of time translation symmetry can occur in periodically driven, Floquet systems with discrete time-translation symmetry. The period of the resulting discrete time crystal (DTC) is quantized to an integer multiple of the drive period, arising from a combination of collective synchronization and many body localization. In this talk, I will describe a simple model for a one dimensional discrete time crystal which explicitly reveals the rigidity of the emergent oscillations as the drive is varied. I will analyze the properties of the dynamical phase transition where the time crystal melts into a trivial Floquet insulator. Effects of long-range interactions and pre-thermalization will be considered in the context of recent DTC realizations in trapped ions and solid-state spins.