Genuine Quantum Effects in Dicke-Type Models at Large Atom Numbers

We investigate the occurrence of genuine quantum effects and beyond mean-field physics in the balanced and unbalanced open Dicke models with a large yet finite number of atoms N. Such driven and dissipative quantum many-body systems have recently been realized in experiments involving ultracold gases inside optical cavities and are known to obey mean-field predictions in the thermodynamic limit N→∞. Here we show quantum effects that survive for large but finite N, by employing a novel open-system dynamics method that allows us to obtain numerically exact quantum dynamical results for atom numbers up to a mesoscopic N≈1000. While we find that beyond-mean-field effects vanish quickly with increasing N in the balanced Dicke model, we are able to identify parameter regimes in the unbalanced Dicke model that allow genuine quantum effects to persist even for mesoscopic N. They manifest themselves in a strong squeezing of the steady state and a modification of the steady-state phase diagram that cannot be seen in a mean-field description. This is due to the fact that the steady-state limit t→∞ and thermodynamic limit N→∞ do not commute.