  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. DTCs promise profound applications in precision time-keeping
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
three over two, realizing a quantum device of measuring the driving frequency
or the interaction strength beyond the Heisenberg limit. Our work paves the way
for designing novel non-equilibrium phases with long coherence time to advance
quantum metrology.
