Observation of parity-time symmetry breaking transitions in a dissipative Floquet system of ultracold atoms.

Open physical systems with balanced loss and gain, described by non-Hermitian parity-time [Formula: see text] reflection symmetric Hamiltonians, exhibit a transition which could engender modes that exponentially decay or grow with time, and thus spontaneously breaks the [Formula: see text]-symmetry. Such [Formula: see text]-symmetry-breaking transitions have attracted many interests because of their extraordinary behaviors and functionalities absent in closed systems. Here we report on the observation of [Formula: see text]-symmetry-breaking transitions by engineering time-periodic dissipation and coupling, which are realized through state-dependent atom loss in an optical dipole trap of ultracold Li atoms. Comparing with a single transition appearing for static dissipation, the time-periodic counterpart undergoes [Formula: see text]-symmetry breaking and restoring transitions at vanishingly small dissipation strength in both single and multiphoton transition domains, revealing rich phase structures associated to a Floquet open system. The results enable ultracold atoms to be a versatile tool for studying [Formula: see text]-symmetric quantum systems.