Phase Control of the Quantum Statistics of Collective Emission

Abstract: We report nonclassical aspects of the collective behaviour of two atoms in a cavity by investigating the photon statistics and photon distribution in a very broad domain of parameters. Starting with the dynamics of two atoms radiating in phase into the cavity, we study the photon statistics for arbitrary interatomic phases as revealed by the second-order intensity correlation function at zero time $g^{(2)}(0)$ and the Mandel $Q$ parameter. We find that the light field can be tuned from antibunched to (super-)bunched as well as nonclassical to classical behaviour by merely modifying the atomic position. The highest nonclassicality in the sense of the smallest $Q$ parameter is found when spontaneous emission, cavity decay, coherent pumping, and atom-cavity coupling are of comparable magnitude. We introduce a quantum version of the negative binomial distribution with its parameters directly related to $Q$ and $g^{(2)}(0)$ and discuss its range of applicability. We also examine the Klyshko parameter which highlights the nonclassicality of the photon distribution.