Photon blockade in the Tavis Cummings model

We use the scattering matrix formalism to study single- and two-photon transport through the Tavis Cummings model as a function of the number of emitters coupling to the cavity mode. It is shown that for a resonant Tavis Cummings system, photon blockade at the output of the cavity mode worsens with the number of emitters while for a detuned Tavis Cummings system, photon blockade at the output of the cavity mode improves with the number of emitters. By explicitly calculating the two-photon scattering properties of this system in the thermodynamic limit of an infinite number of emitters, we show that the light emitted from Tavis Cumming system under excitation by a coherent drive transitions from bunching to anti-bunching as the emitters are detuned from the cavity mode. Finally, we analyze the impact of inhomogeneous broadening in the emitter frequencies on both resonant and detuned photon blockade through the Tavis Cumming system.