The paper by Birnbaum et al. provides an expanded discussion on photon blockade in an optical cavity strongly coupled to a single trapped atom. Photon blockade, first proposed in analogy with Coulomb blockade for electrons, occurs when the absorption of one photon by an optical device blocks the transmission of another, leading to nonclassical output photon statistics. The authors revisit the theoretical model and results presented in their previous work, focusing on the general phenomenology of photon blockade and the specific system they studied. Key points include: 1. **General Considerations**: The authors define photon blockade in terms of transmission coefficients for photon number states, where the transmission of a second photon is blocked if \( |t_n| < |t_1|^n \) for \( n \geq 2 \). 2. **Eigenvalues of the Atom-Cavity System**: They analyze the eigenvalue structure of the atom-cavity system, considering a single atom coupled to a cavity with two degenerate orthogonal linear modes. The eigenvalues are calculated and their implications for photon statistics are discussed. 3. **Driven Atom**: The authors explore the effect of driving the atom directly instead of the cavity, showing that the driven atom system exhibits different photon statistics compared to the cavity. 4. **Birefringence and Stark Shifts**: They extend the model to include cavity birefringence and ac-Stark shifts, modifying the Hamiltonian and analyzing the impact on the transmitted field and intensity correlation functions. 5. **Discussion**: The paper concludes by discussing the criteria for photon blockade, the coherence requirements, and the implications for pulsed excitation. The study provides a comprehensive framework for understanding photon blockade in this system, highlighting the complex dynamics and the importance of various physical mechanisms.The paper by Birnbaum et al. provides an expanded discussion on photon blockade in an optical cavity strongly coupled to a single trapped atom. Photon blockade, first proposed in analogy with Coulomb blockade for electrons, occurs when the absorption of one photon by an optical device blocks the transmission of another, leading to nonclassical output photon statistics. The authors revisit the theoretical model and results presented in their previous work, focusing on the general phenomenology of photon blockade and the specific system they studied. Key points include: 1. **General Considerations**: The authors define photon blockade in terms of transmission coefficients for photon number states, where the transmission of a second photon is blocked if \( |t_n| < |t_1|^n \) for \( n \geq 2 \). 2. **Eigenvalues of the Atom-Cavity System**: They analyze the eigenvalue structure of the atom-cavity system, considering a single atom coupled to a cavity with two degenerate orthogonal linear modes. The eigenvalues are calculated and their implications for photon statistics are discussed. 3. **Driven Atom**: The authors explore the effect of driving the atom directly instead of the cavity, showing that the driven atom system exhibits different photon statistics compared to the cavity. 4. **Birefringence and Stark Shifts**: They extend the model to include cavity birefringence and ac-Stark shifts, modifying the Hamiltonian and analyzing the impact on the transmitted field and intensity correlation functions. 5. **Discussion**: The paper concludes by discussing the criteria for photon blockade, the coherence requirements, and the implications for pulsed excitation. The study provides a comprehensive framework for understanding photon blockade in this system, highlighting the complex dynamics and the importance of various physical mechanisms.