Time crystals: analysis of experimental conditions

TL;DR

This paper analyzes the experimental conditions necessary for realizing discrete time crystals in ultra-cold atom systems, highlighting their potential for observing symmetry breaking, quantum phase transitions, and localization effects in the time domain.

Contribution

It provides a detailed theoretical analysis of experimental setups for creating discrete time crystals with ultra-cold atoms bouncing on oscillating or randomly moving mirrors.

Findings

Conditions for spontaneous symmetry breaking in time crystals.

Possibility of observing dynamical quantum phase transitions.

Potential to observe Anderson localization effects in the time domain.

Abstract

Time crystals are quantum many-body systems which are able to self-organize their motion in a periodic way in time. Discrete time crystals have been experimentally demonstrated in spin systems. However, the first idea of spontaneous breaking of discrete time translation symmetry, in ultra-cold atoms bouncing on an oscillating mirror, still awaits experimental demonstration. Here, we perform a detailed analysis of the experimental conditions needed for the realization of such a discrete time crystal. Importantly, the considered system allows for the realization of dramatic breaking of discrete time translation symmetry where a symmetry broken state evolves with a period tens of times longer than the driving period. Moreover, atoms bouncing on an oscillating mirror constitute a suitable system for the realization of dynamical quantum phase transitions in discrete time crystals and for the demonstration of various non-trivial condensed matter phenomena in the time domain. We show that Anderson localization effects, which are typically associated with spatial disorder and exponential localization of eigenstates of a particle in configuration space, can be observed in the time domain when ultra-cold atoms are bouncing on a randomly moving mirror.