Exploring photon blockade in a two-photon Jaynes-Cummings model with atom and cavity drivings

We explore a method for achieving photon blockade (PB) through a two-photon Jaynes-Cummings (JC) model that includes both cavity and atom drivings. Analytical expressions for the steady state are derived to calculate photon-number distribution and correlation functions. Based on this analysis, we establish the theoretical conditions required for generating PB by controlling both drivings and propose a scheme to identify conventional photon blockade (CPB) and unconventional photon blockade (UPB) by analyzing the second- and third-order correlation functions. We validate our findings through numerical simulations conducted in an artificial atom system. We discuss two cases, one in which the transition frequency of the two-level atom is in two-photon resonance with the cavity frequency and the other in which it is off-resonance. We observe a significant interplay between CPB and UPB effects in the resonant case. In the off-resonance case, we demonstrate that UPB can be achieved by manipulating the strengths of atom driving and cavity driving to satisfy a specific relationship while meeting the requirements for optimal detuning relations. This work provides essential insights into controlling the PB effect using the two-photon JC model with both the atom and cavity drivings.