Collective Excitations of Dissipative Time Crystals

TL;DR

This paper investigates the excitation spectrum of atoms in a dissipative optical cavity undergoing a transition to a time-crystalline phase, using Floquet theory and an effective master equation, with implications for experimental detection.

Contribution

It introduces a novel analysis of the excitation spectrum across phase transitions in dissipative time crystals using an effective atom-only master equation.

Findings

Identification of spectral features at phase transitions

Characterization of stable oscillations in the time-crystalline phase

Proposals for experimental detection via cavity probing

Abstract

We study the dynamics of atoms interacting periodically with a dissipative optical cavity and employ Floquet theory to analyze their low-frequency behavior. By means of an effective atom-only master equation, valid in the bad cavity regime, we characterize the excitation spectrum of the atoms across the transition from a normal phase to a time-crystalline phase where the atoms undergo stable oscillations. We identify features in the complex excitation spectra when crossing second and first order transitions where the order parameter changes continuously or abruptly. Finally, we discuss how these results can be detected experimentally by probing the cavity with an additional drive. Our work provides important tools for analyzing the response of dynamical out-of-equilibrium phases.