The role of atomic interactions in cavity-induced continuous time crystals

Abstract

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 that 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 resembles the one proposed for preheating of 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.

Figures (3)

• Figure 1: The critical frequency of the instability is shown in the lower plot of a) as a function of $\Delta$ and $\kappa$. By tuning $\Delta$ the critical mode change from exhibiting static to oscillating superradiance and a purely atomic instability over a large range of cavity loss rates. Above the critical frequency and coupling is shown along the white dashed line. The upper plot shows the critical frequency and coupling along the dashed line in the lower plot. In b) the sign of the cubic interaction as a function of $\Delta$ and $U$ is plotted for $\kappa=0.4E_R$. This determines the stability of the symmetry-broken state beyond the linear analysis. For for the entire figure $\delta=0.2 E_R$.
• Figure 2: a) The dynamic nature of the OSR phases combined with finite atom-interaction leads to occupation of atom modes out of the center manifold, through the symmetric and asymmetric process illustrated here. b) The scaling of the growth rates, computed from the Floquet quasi-energies of the linearized equations, for the asymmetric channel marked with orange stars, with a square-root fit (orange line) and the scaling of symmetric channel marked with red stars, with a linear fit (red line). The same parameters as in \ref{['fig:melting']} have been used.
• Figure 3: The lower plot shows the exponential growth rates of the atomic modes outside of the center manifold. The parameters are equivalent to those in \ref{['fig:lcPD']} with $\Delta=0.6E_R$ resulting in $\omega_c=0.586E_R$, and we choose $U=0.01E_R$. The orange ticks indicate the predicted momentum based on the asymmetric channel, while the red tick signifies the symmetric channel momentum. The green tick is the atom mode coupled to the symmetric channel through the cavity. The upper plot shows the resulting atom distribution after 200 periods at the dashed line in the lower plot, both with numerical integration of \ref{['eq:atomEOM', 'eq:cavityEOM']} in blue and from the linearized prediction with the dashed green line.