Fractional Time Crystals. (arXiv:1812.10923v3 [cond-mat.quant-gas] UPDATED)
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.