Generation and Enhancement of Bipartite and Tripartite Entanglement in an Electro-Optomechanical Ring Cavity

This paper investigates the generation and control of multipartite quantum entanglement within a hybrid electro-optomechanical ring cavity. The system architecture features three mechanical oscillators—two of which are charged and coupled via Coulomb forces—integrated with an optical cavity containing an optical parametric amplifier (OPA). By deriving the system's Hamiltonian and solving the linearized quantum Langevin equations, the authors analyze how the interplay between radiation pressure, Coulomb coupling, and parametric nonlinearity can be harnessed to generate and amplify quantum correlations.

The researchers employ a covariance matrix formalism to quantify entanglement. Bipartite entanglement is measured using logarithmic negativity, while tripartite entanglement is assessed through the minimum residual contangle. The study systematically explores the impact of experimental parameters, including OPA gain and phase, laser detuning, and input power. By treating the OPA as a synthetic control knob, the authors demonstrate that they can dynamically sculpt the system's Hamiltonian to optimize entanglement levels, providing a theoretical framework for managing multipartite states in hybrid quantum platforms.

The analysis reveals that while Coulomb interaction is essential for the initial generation of entanglement between mechanical resonators, the OPA acts as a powerful amplifier for these correlations. The authors show that the degree of entanglement is highly sensitive to the OPA's gain and phase, allowing for precise tuning. However, a significant finding is the existence of a stability trade-off: the parameter configurations that yield the highest entanglement levels often push the system toward the boundaries of its stable operating regime. Furthermore, the study confirms that thermal noise acts as a persistent limiting factor, necessitating low-temperature environments to maintain the integrity of the generated quantum states.