Controlled preparation of phases in two-dimensional time crystals

TL;DR

This paper explores the phases of two-dimensional time crystals in driven many-body systems, providing methods to realize specific phases and linking them to Hubbard lattice models for quantum simulation.

Contribution

It introduces a practical approach to control and prepare different phases of 2D time crystals, connecting them to many-body lattice models for quantum simulation.

Findings

Identification of various phases in 2D time crystals

Method for optimal initial conditions and parameters

Mapping to Hubbard lattice models for quantum simulation

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.