# Fractional Time Crystals

## TL;DR

This paper demonstrates that ultra-cold atoms bouncing on an oscillating mirror can spontaneously form fractional discrete time crystals with motion periods that are rational multiples of the driving period, using higher order resonant driving.

## Contribution

It introduces a novel approach to analyze fractional discrete time crystals formed through higher order resonant driving in a cold atom system.

## Key findings

- Fractional time crystals can be realized with ultra-cold atoms and oscillating mirrors.
- Higher order resonant driving enables formation of rational period ratios.
- The system exhibits spontaneous symmetry breaking in the time domain.

## Abstract

Time crystals are quantum systems which are able to reveal condensed matter behavior in the time domain. It is known that crystalization in time can be observed in a periodically driven many-body system when interactions between particles force a system to evolve with a period which is an integer multiple of a driving period. This phenomenon is dubbed discrete time crystal formation. Here, we consider ultra-cold atoms bouncing on an oscillating atom mirror and show that the system can spontaneously form a discrete time crystal where the ratio of a period of its motion and a driving period is a rational number. This kind of discrete time crystals requires higher order resonant driving which is analyzed here with the help of an original approach.