Discrete time crystals: rigidity, criticality, and realizations

TL;DR

This paper investigates the properties, phase diagram, and experimental realization of one-dimensional discrete time crystals, highlighting their rigidity, phase transition, and potential implementation with trapped ions.

Contribution

It introduces a simple model for 1D discrete time crystals, maps their phase diagram, and proposes a feasible experimental realization with trapped ions.

Findings

Rigidity of oscillations demonstrated in the model

Phase diagram and transition properties mapped

Blueprint for experimental realization with trapped ions proposed

Abstract

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 is quantized to an integer multiple of the drive period, arising from a combination of collective synchronization and many body localization. Here, we consider a simple model for a one dimensional discrete time crystal which explicitly reveals the rigidity of the emergent oscillations as the drive is varied. We numerically map out its phase diagram and compute the properties of the dynamical phase transition where the time crystal melts into a trivial Floquet insulator. Moreover, we demonstrate that the model can be realized with current experimental technologies and propose a blueprint based upon a one dimensional chain of trapped ions. Using experimental parameters (featuring long-range interactions), we identify the phase boundaries of the ion-time-crystal and propose a measurable signature of the symmetry breaking phase transition.