  In our recent paper [1], we reported observations of photon blockade by one
atom strongly coupled to an optical cavity. In support of these measurements,
here we provide an expanded discussion of the general phenomenology of photon
blockade as well as of the theoretical model and results that were presented in
Ref. [1]. We describe the general condition for photon blockade in terms of the
transmission coefficients for photon number states. For the atom-cavity system
of Ref. [1], we present the model Hamiltonian and examine the relationship of
the eigenvalues to the predicted intensity correlation function. We explore the
effect of different driving mechanisms on the photon statistics. We also
present additional corrections to the model to describe cavity birefringence
and ac-Stark shifts. [1] K. M. Birnbaum, A. Boca, R. Miller, A. D. Boozer, T.
E. Northup, and H. J. Kimble, Nature 436, 87 (2005).
