Formation of Complex Discrete Time Crystals with Ultracold Atoms

TL;DR

This paper demonstrates the formation of complex discrete time crystals in ultracold atomic systems driven by an oscillating mirror, showing spontaneous symmetry breaking and cascade effects due to intra- and inter-species interactions.

Contribution

It introduces a novel setup with two ultracold atomic clouds and infinite inter-species repulsion, revealing complex time crystal formation and cascade symmetry breaking.

Findings

Strong intra-species attraction induces time translation symmetry breaking.

Cascade of symmetry breaking occurs from the upper to the lower cloud.

Complex time crystals evolve with periods different from the driving period.

Abstract

We study discrete time crystal formation in a system driven periodically by an oscillating atomic mirror, consisting of two distinct ultracold atomic clouds in the presence of a gravitational field. The intra-species interactions are weak and attractive, while the inter-species interactions are infinitely strong and repulsive. The clouds are arranged in a one-dimensional stack, where the bottom cloud bounces on an oscillating atomic mirror, which effectively acts as a driving force for the upper cloud due to the infinite inter-species repulsion. Using a Jastrow-like variational ansatz for the many-body wavefunction, we show that sufficiently strong attractive intra-species interactions drive each subsystem to spontaneously break discrete time translation symmetry, resulting in the formation of a complex discrete time crystal evolving with a period different than the driving period. Since the bottom cloud serves as the effective periodic driving for the upper cloud, this leads to a cascade of spontaneous symmetry breaking. With increasing intra-species interactions, we first observe a pronounced effect of spontaneous time translation symmetry breaking in the upper cloud, followed by a similar effect in the lower atomic cloud.