# An eternal discrete time crystal beating the Heisenberg limit

## TL;DR

This paper demonstrates a robust all-to-all interaction-based discrete time crystal that avoids thermalization, maintains coherence, and surpasses the Heisenberg limit in sensitivity, advancing quantum metrology and non-equilibrium phase design.

## Contribution

It introduces a new type of DTC with all-to-all interactions that resists thermalization and achieves super-Heisenberg scaling in sensitivity.

## Key findings

- DTC maintains coherence despite inhomogeneous driving.
- Sensitivity scales with particle number to the 3/2 power.
- DTC evades thermalization and enhances quantum metrology.

## 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. 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.