Anomalous dependence of sensitivity on observation time caused by memory retention in the time crystal

TL;DR

This paper investigates how memory effects in a time crystal system influence its sensitivity to perturbations, revealing an anomalous quadratic dependence on observation time in certain regimes, with implications for sensing and metrology.

Contribution

It demonstrates the anomalous quadratic sensitivity dependence caused by memory retention in a time crystal, expanding potential applications in sensing and measurement.

Findings

Sensitivity scales quadratically with observation time in the time crystal regime.

Memory retention enables enhanced sensitivity compared to normal states.

Transition areas show a mixed sensitivity behavior.

Abstract

In this work, we consider a composite atom-cavity system interacting with a ring resonator. In such a structure, time crystal regime can be observed. We show that a quadratic observation time dependence of the system's sensitivity to perturbations takes place in the time crystal regime and also in the transition area to the normal state. This dependence is due to ability of the system to retain the memory of the atom's initial state. Outside these areas, the system is not able to retain the memory of the atom's initial state and the sensitivity scales linearly on the observation time. Our results open up a new way for implementation of discrete time crystals in sensing and metrology.