  It is known that the 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.
