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A discrete time crystal (DTC) repeats itself with a rigid rhythm, mimicking aticking clock set by the interplay between its internal structures and anexternal force. DTCs promise profound applications in precision time-keepingand other quantum techniques. However, it has been facing a grand challenge ofthermalization. The periodic driving supplying the power may ultimately bringDTCs to thermal equilibrium and destroy their coherence. Here, we show that anall-to-all interaction delivers a DTC that evades thermalization and maintainsquantum coherence and quantum synchronization regardless of spatialinhomogeneities in the driving field and the environment. Moreover, thesensitivity of this DTC scales with the total particle number to the power ofthree over two, realizing a quantum device of measuring the driving frequencyor the interaction strength beyond the Heisenberg limit. Our work paves the wayfor designing novel non-equilibrium phases with long coherence time to advancequantum metrology.

An eternal discrete time crystal beating the Heisenberg limit