Spontaneous breaking of time translation symmetry in a system without periodic external driving.

It is known that spontaneous time translation symmetry-breaking can occur in systems periodically driven at a certain period. We predict a spontaneous breaking of time translation symmetry in an atom-cavity system without external driving, in which a time scale is determined by the time of light bypass of the resonator. We demonstrate that there is a parameter range, in which a system state returns to its initial state only after two bypasses of the resonator. We believe that the predicted phenomenon opens a way to a new direction in the time crystal field.