This paper presents a detailed discussion of photon blockade in an optical cavity with a single trapped atom. The authors report observations of photon blockade, where the absorption of a first photon blocks the transmission of a second, leading to non-classical photon statistics. The phenomenon is explained through the interaction of a single two-level atom with an optical cavity, where the Jaynes-Cummings ladder of eigenstates leads to anharmonicity and photon blockade. The authors describe the general condition for photon blockade in terms of transmission coefficients for photon number states and examine the relationship of eigenvalues to the predicted intensity correlation function. They explore the effect of different driving mechanisms on photon statistics and present additional corrections to the model to account for cavity birefringence and ac-Stark shifts. The paper also discusses the eigenvalue structure of the atom-cavity system, the effect of driving the cavity or the atom, and the role of cavity birefringence and ac-Stark shifts in modifying the transmission and intensity correlation functions. The authors conclude that their results support the criteria for photon blockade, with the intensity correlation function showing sub-Poissonian statistics for certain probe frequencies. The paper also discusses the implications of photon blockade for quantum information processing and the challenges of achieving high efficiency in practical applications.This paper presents a detailed discussion of photon blockade in an optical cavity with a single trapped atom. The authors report observations of photon blockade, where the absorption of a first photon blocks the transmission of a second, leading to non-classical photon statistics. The phenomenon is explained through the interaction of a single two-level atom with an optical cavity, where the Jaynes-Cummings ladder of eigenstates leads to anharmonicity and photon blockade. The authors describe the general condition for photon blockade in terms of transmission coefficients for photon number states and examine the relationship of eigenvalues to the predicted intensity correlation function. They explore the effect of different driving mechanisms on photon statistics and present additional corrections to the model to account for cavity birefringence and ac-Stark shifts. The paper also discusses the eigenvalue structure of the atom-cavity system, the effect of driving the cavity or the atom, and the role of cavity birefringence and ac-Stark shifts in modifying the transmission and intensity correlation functions. The authors conclude that their results support the criteria for photon blockade, with the intensity correlation function showing sub-Poissonian statistics for certain probe frequencies. The paper also discusses the implications of photon blockade for quantum information processing and the challenges of achieving high efficiency in practical applications.