Exploring Photon Blockade in Multimode Jaynes-Cummings Models with Two-Photon Dissipation

The photon blockade phenomenon, a promising tool for realizing efficient single-photon sources, is the central focus of our work. We study this phenomenon within the context of the multimode extension of the Jaynes-Cummings model, incorporating two-photon dissipation and external coherent driving. Operating in the weak-driving regime, we confine our analysis to the two-excitation sector of the Hilbert space, initially exploring the single-mode case and then focusing on the corresponding multimode problem. Our study calculates the second-order correlation function (both numerically and analytically) for zero- and nonzero time delays in single- and multimode cases, to pinpoint and validate the conditions that lead to conventional and unconventional photon blockade. Our zero delay findings reveal that photon antibunching is comparable in both cases; however, the multimode case offers a greater degree of control and applicability. Furthermore, for non-zero delay operation, we find that when one of the multiple modes is set at the optimal conventional photon blockade conditions, the behavior of the curve mimics the single-mode problem with an overall slower rate of reaching the $g^{(2)}(\tau)=1$ value. These results highlight the practical implications of our findings for building useful single-photon sources.