Condensed matter physics in big discrete time crystals

TL;DR

This paper reviews how ultracold atom bouncing systems can simulate condensed matter phenomena in the time domain, including localization, topological phases, and complex lattice structures, advancing the study of temporal quantum matter.

Contribution

It introduces the concept of using bouncing Bose-Einstein condensates to realize and explore a wide range of condensed matter phenomena in the time dimension, including novel lattice geometries.

Findings

Demonstration of discrete time crystals with up to 100 temporal sites

Observation of Anderson localization and topological phases in time

Construction of multi-dimensional time lattices with complex geometries

Abstract

We review the application of discrete time crystals created in a Bose-Einstein condensate (BEC) of ultracold atoms bouncing resonantly on an oscillating mirror to the investigation of condensed matter phenomena in the time dimension. Such a bouncing BEC system can exhibit dramatic breaking of time-translation symmetry, allowing the creation of discrete time crystals having up to about 100 temporal lattice sites and suitable for hosting a broad range of temporal condensed matter phenomena. We first consider single-particle condensed matter phenomena in the time dimension which include Anderson localization due to temporal disorder, topological time crystals, and quasi-crystal structures in time. We then discuss many-body temporal condensed matter phenomena including Mott insulator phases in time, many-body localization in time, many-body topological time crystals and time crystals having long-range exotic interactions. We also discuss the construction of two (or three) dimensional time lattices, involving the bouncing of a BEC between two (or three) orthogonal oscillating mirrors and between two oscillating mirrors oriented at 45-degrees. The latter configuration supports a versatile M\"obius strip geometry which can host a variety of two-dimensional time lattices including a honeycomb time lattice and a Lieb square time lattice. Finally, we discuss the construction of a six-dimensional time-space lattice which is based on periodically driven BECs trapped in a three-dimensional optical lattice.