In the field of quantum information science, feedback control has become an important method for preparing and manipulating nonclassical beams. Here we theoretically propose an active nonlinear feedback control system utilizing two four-wave-mixing processes ${\text{FWM}}_1$ and ${\text{FWM}}_2$ with spatially structured pumping, where the second four-wave-mixing process ${\text{FWM}}_2$ acts as an active nonlinear controller. After considering practical losses, the input-output relation of the system is derived. The effects of the feedback strength, the phase of the feedback loop, and the gain of the ${\text{FWM}}_1$ on the relative intensity-difference squeezing (IDS) of the nonlinear feedback control system are investigated theoretically. Remarkably, we find that even when the ${\text{FWM}}_1$ operates at a significantly low level of pump power, the degree of the IDS across all six output fields of the system is enhanced for a certain range of intensity gain and phase. Moreover, there exists an optimal intensity gain and phase to maximize the IDS. In addition, we analyze the entanglement properties of the system by applying the partial transpose criterion and find that the intensity gain and phase can tailor the entanglement structure of the hexapartite state. Our results highlight a promising strategy for improving the fidelity of quantum communication and for enhancing the measurement precision in quantum metrology.

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• Quantum feedback
• Quantum information processing
• Quantum optics