Lamb shift statistics in mesoscopic quantum ensembles

Ensembles of two-level systems interacting with a single-mode electromagnetic field are increasingly being used for the development quantum information processors and mesoscopic devices. These characterized by set energy-level hybridizations, split Lamb shifts, that occur when ensemble mode interact coherently high cooperativity. For dimensions simulating system dynamics while including complete shifts is generally intractable. We present compact description shift statistics behavior across all collective angular momentum excitation subspaces without resorting to overly restrictive approximations state space. also calculate averaged effective weighted over degeneracies these connect our results experiments.