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Enhanced multi-parameter metrology in dissipative Rydberg atom time crystals

The pursuit of unprecedented sensitivity in quantum enhanced metrology has spurred interest in non-equilibrium quantum phases of matter and their symmetry breaking. In particular, criticality-enhanced metrology through time-translation symmetry breaking in many-body systems, a distinct paradigm compared to spatial symmetry breaking, is a field still in its infancy. Here, we have investigated the enhanced sensing at the boundary of a continuous time-crystal (CTC) phase in a driven Rydberg atomic gas. By mapping the full phase diagram, we identify the parameter-dependent phase boundary where the time-translation symmetry is broken. This allows us to use a single setup for measuring multiple parameters, in particular frequency and amplitude of a microwave field. By increasing the microwave field amplitude, we first observe a phase transition from a thermal phase to a CTC phase, followed by a second transition into a distinct CTC state, characterized by a different oscillation frequency. Furthermore, we reveal the precise relationship between the CTC phase boundary and the scanning rate, displaying enhanced precision beyond the Standard Quantum Limit. This work not only provides a promising paradigm rooted in the critical properties of time crystals, but also advances a method for multi-parameter sensing in non-equilibrium quantum phases.