Effects of cavity loss rate and lattice depth per photon on continuous time crystals in an atom-cavity system

Abstract

We investigate a newly observed dynamical phase known as continuous time crystals appearing as limit cycle phases in an atom-cavity system. This phase can be realised for sufficiently strong blue-detuned pump intensity and is characterised by oscillations of the intracavity photon number. Here, we study within the mean-field theory the stability of limit cycles in a one-dimensional atom-cavity system for varying cavity field decay rate and cavity lattice depth per photon, also known as the light shift. We find that the area of stability of the limit cycle in the relevant parameter space increases for smaller light shifts and intermediate values of photon decay rate.