Fractional time crystals

Time crystals are quantum systems that are able to reveal condensed matter behavior in the time domain. It is known that crystallization in time can be observed in a periodically driven many-body system when interactions between particles force a system to evolve with a period that is an integer multiple of a driving period. This phenomenon is dubbed discrete time crystal formation. Here, we consider ultracold 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 crystal requires higher-order resonant driving, which is analyzed here with the help of an original approach.