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Enhanced Microwave Sensing with Dissipative Continuous Time Crystals

A dissipative time crystal is an emergent phase in driven-dissipative quantum many-body systems, characterized by sustained oscillations that break time-translation symmetry spontaneously. Here, we explore nonequilibrium phase transitions in a dissipative Rydberg system driven by a microwave (MW) field and demonstrate their critical sensitivity to high-precision MW sensing. Distinct dynamical regimes are identified, including monostable, bistable, and oscillatory phases under mean-field coupling. Unlike single-particle detection--where the beating signal decays linearly with MW field strength--the time crystalline phase exhibits high sensitivity to MW perturbations, with rapid, discontinuous frequency switching near the monostable-oscillatory boundary. The abrupt transition is rooted in spontaneous symmetry breaking in time and is fundamentally insensitive to the background noise. On this basis, a minimum detectable MW field strength on the order of 1nV/cm is achieved by leveraging this sensitivity. Our results establish a framework for controlling time crystalline phases with external fields and advance MW sensing through many-body effects.