We consider continuous time-crystalline phases in dissipative many-body systems of atoms in cavities, focusing on the role of short-range interatomic interactions. First, we show that the latter can alter the nature of the time crystal by changing the type of the underlying critical bifurcation. Second, we characterize the heating mechanism and dynamics resulting from the short-range interactions and demonstrate that they make the time crystal inherently metastable. We argue this is generic for the broader class of dissipative time crystals in atom-cavity systems whenever the cavity loss rate is comparable to the atomic recoil energy. We observe that such a scenario for heating has several similarities to the one proposed for preheating in the early universe, where the oscillating coherent inflation field decays into a cascade of exponentially growing fluctuations. By extending approaches for dissipative dynamical systems to our many-body problem, we obtain analytical predictions for the parameters describing the phase transition and the heating rate inside the time-crystalline phase. We underpin and extend the analytical predictions of the heating rates with numerical simulations, which also show that the metastable regime exists when the inherent stochastic nature is taken into account}.
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Author comments upon resubmission
We have implemented the referees comment and in particular this lead to adding a new section focusing on the numerical solution of the full equations. Here it was additional shown how the previous conclusions are stable against realistic noise levels.
List of changes
1) Added sentence about stability towards noise in abstract. Line: 17-19 2) Explained structure of paper. Line: 59-70 3) Additional paragraph discussing validity of model. Line: 100-109 4) Skecthed linear expansion method: 119-122 5) Clarified different superradiant phases. Line: 122-131 + 150-151 6) Made AI critieria more transparent. Line: 135-138 7) Changed title of section 4 to: "Energy redistribution" 8) Expanded upon the the effect of NCM modes vs. CM modes. Line: 201-213 9) Added paragraph to clarify the nature of the energy redistrubution mechanism and how it is approximated. Line: 216-226 10) Included new variables to better highlight the difference between the assymetric and symmetric scattering channels. Line: 232 + 237 11) Fixed typo in $\omega_c$ inequality. Line: 233 12) Added paragraph highlighting the small occupation of the NCM modes in the numerical results presented section 4. Line: 255-260 13) Added new section 5 titled "Metastable nature of time crystal". This section highlights the metastable nature of the TC through a careful numerical investigation and shows that the results are also stable towards noise. Line: 261-375 14) New paragraph in the conclusion highlight phenomonolgy behind our results. Line: 382-405 15) Clarified initial reference in Appendix A. Line: 413-417
