Supplemental Information – Photon Blockade in an Optical Cavity with One Trapped Atom

In our Letter [1], we employ a model of a two mode cavity coupled to an atom with multiple internal states. In this Supplement we make explicit the coupling used in the model Hamiltonian to determine the eigenvalues displayed in Figure 1(b) of Ref. [1]. This Hamiltonian was also incorporated into the master equation for the damped, driven system used to compute the theoretical results in Fig. 2(b) of Ref. [1]. We furthermore present an extension to this model which includes the effect of cavity birefringence and FORT induced ac-Stark shifts in the atomic states. The modified cavity transmission and intensity correlation function are presented for comparison. We approximate the atom-cavity coupling to be a dipole interaction. We define the atomic dipole transition operators for the 6S1/2, F = 4 → 6P3/2, F ′ = 5′ transition in atomic Cæsium as