Quantum statistics of light transmitted through an intracavity Rydberg medium

We theoretically investigate the quantum statistical properties of light transmitted through an atomic medium with strong optical non-linearity induced by Rydberg-Rydberg van der Waals interactions. In our setup, atoms are located in a cavity and non-resonantly driven on a two-photon transition from their ground state to a Rydberg level via an intermediate state by the combination of the weak signal field and a strong control beam. To characterize the transmitted light we compute the second-order correlation function $g^{\left(2\right)}\left(\tau\right)$. The simulations we obtained on the specific case of rubidium atoms suggest that the bunched or antibunched nature of the outgoing beam can be chosen at will by appropriately tuning the physical parameters.