Abstract
The study of phases is useful for understanding novel states of matter. One such state of matter are time crystals which constitute periodically driven interacting many-body systems that spontaneously break time translation symmetry. Time crystals with arbitrary periods (and dimensions) can be realized using the model of Bose-Einstein condensates bouncing on periodically-driven mirror(s). In this work, we identify the different phases that characterize the two-dimensional time crystal. By determining the optimal initial conditions and value of system parameters, we provide a practical route to realize a specific phase of the time crystal. These different phases can be mapped to the many-body states existing on a two-dimensional Hubbard lattice model, thereby opening up interesting opportunities for quantum simulation of many-body physics in time lattices.
Highlights
The ability to trap ultracold atomic gases and control their interactions with high precision has lead the way towards the realization of new phases of matter [1,2,3,4]
The main result of our work is the identification of the different phases that characterize the discrete time crystal in two dimensions
We characterize the different phases realizable in a time crystal that maps to a 2D lattice model
Summary
The ability to trap ultracold atomic gases and control their interactions with high precision has lead the way towards the realization of new phases of matter [1,2,3,4]. We can simplify the optimization task by approximating the many-body wave function as a single quantum wave packet thereby reducing the control parameters to a manageable number of six consisting of initial position, momentum, and size of the wave packet determined by the 2D harmonic trap in which the condensate is initially stored, see Fig. 1(a) This approximation is justified in the mean-field limit for the gas of bosonic atoms if the time required to prepare the initial state is much shorter than the overall dynamics of the discrete time crystal.
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