Bipartite entanglement generation in an electro-optomechanical ring cavity via charge-mediated coupling

We present a theoretical investigation of quantum entanglement enhancement in an electro-optomechanical system comprising a ring cavity with two Coulomb-coupled mechanical resonators and an embedded optical parametric amplifier (OPA). The system dynamics are governed by radiation pressure interactions between the optical field and mechanical modes, modified by both the Coulomb coupling and OPA-induced squeezing. Through a comprehensive quantum Langevin analysis and linearization approach, we demonstrate how these competing interactions can be exploited to generate and control entanglement. Our key finding is that the Coulomb interaction strength is fundamental for generating bipartite entanglement, both between directly coupled mechanical modes and, more remarkably, between optical and mechanical modes, thereby influencing the entire system. The OPA parameters, namely the gain and phase, provide powerful control knobs for entanglement optimization. Notably, the OPA enhances entanglement robustness against thermal noise, resulting in stronger quantum correlations. We quantify these effects through covariance matrix methods and logarithmic negativity measures. The study provides new insights into hybrid optomechanical entanglement generation, showing how combined charge-mediated coupling and optical squeezing can overcome typical limitations of purely optomechanical systems. These results offer practical guidelines for experimental implementations in quantum information processing and macroscopic quantum state engineering, particularly in systems where environmental noise and parameter stability are critical concerns.