Eternal discrete time crystal beating the Heisenberg limit

Abstract

A discrete time crystal (DTC) repeats itself with a rigid rhythm, mimicking a ticking clock set by the interplay between its internal structures and an external force. Discrete time crystals promise profound applications in precision timekeeping and other quantum techniques. However, it has been facing a grand challenge of thermalization. The periodic driving supplying the power may ultimately bring DTCs to thermal equilibrium and destroy their coherence. Here we show that an all-to-all interaction delivers a DTC that evades thermalization and maintains quantum coherence and quantum synchronization regardless of spatial inhomogeneities in the driving field and the environment. Moreover, the sensitivity of this DTC scales with the total particle number to the power of 3/2, realizing a quantum device of measuring the driving frequency or the interaction strength beyond the Heisenberg limit. Our work paves the way for designing nonequilibrium phases with long coherence time to advance quantum metrology.