Fig. 1. (a) The scheme of coherent feedback control system based on the cascade four wave mixing processes; (b) The Double-Λ type transition energy-level diagram of ⁸⁵Rb D1 line. ∆ corresponds to one-photon detuning, δ corresponds to two-photon detuning.

Fig. 2. The coherent feedback system based on the cascaded four wave mixing processes. The green dashed frame is the optical transmission loss model in the feedback loop, and the pink dashed frames are the loss model of atomic absorption.

Fig. 3. (a) (b) (c) correspond to the smallest symplectic eigenvalues of the three bipartitions varying with the value of phase and reflectivity, respectively.

Fig. 4. (a)(b)(c)(d) show the relationship between the intensity of three output fields and the phase ϕ under different gains condition, respectively. Here, k = 0.5, .

Fig. 5. (a) (b) (c) correspond to the smallest symplectic eigenvalues of the three bipartitions varying with the value of gain and reflectivity, respectively.

Fig. 6. The smallest symplectic eigenvalues of the three bipartitions vary with reflectivity when ϕ is taken the value of 180° and G = 3, 5.