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

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.