Quantum signatures of collective behavior of a coherently driven two atom system coupled to a single-mode of the electromagnetic field

We present a study of the quantum statistical properties of light emitted by two coherently driven atoms coupled to a single-mode cavity, an ideal setup to precisely investigate various aspects of collective behavior over a wide range of couplings to cavity and external drive. At high pumping and coupling, we predict the possibility of steady-state hyperradiance accompanied by (super-)bunching for an out of phase radiation. The mean photon number can be up to $2$ orders of magnitude higher than in the single atom case. The highest nonclassicality in the sense of the smallest Mandel $Q$ parameter is found when spontaneous emission, cavity decay, coherent pumping, and atom-cavity coupling are comparable. A quantum version of the negative binomial distribution with parameters directly related to $Q$ characterizes the photon distribution in the cavity and its quantum features.