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

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