Generation of multimode quantum correlation with energy-level cascaded four-wave mixing processes

Multimode quantum correlation has important applications in the field of quantum information. In this paper, we propose a compact scheme to generate multiple quantum correlated beams based on energy-level cascaded four-wave mixing (EC-FWM) process in a single atomic medium of rubidium. Injecting two strong pump beams with different frequencies and one weak probe beam into one rubidium vapor, four possible parametrically amplified FWM (PA FWM) processes can coexist under different phase matching conditions. Within the scheme, the weak probe beam is amplified and three coherent beams are generated, which can also be seen as an eight-wave mixing (EWM) process when certain phase matching condition is satisfied. Based on the energy level system of the scheme, three different cascaded structure models are employed to study the quantum correlation between the four generated beams. Amplitude and phase quadratures squeezing and intensity squeezing of the three- and four-mode are calculated via the input–output relations of the system. We found versatile multimode squeezing can be generated in all the structures, but the degree of squeezing and its distribution among the modes are different, depending on the specific structure. Furthermore, the relation of the quantum correlation, as well as the eigenmodes and eigenvalues of the four-mode quantum states are studied.