Boosting macroscopic entanglement in charged cavity optomechanical system through coherent feedback loop

In this paper, we propose a scheme to boost a macroscopic entanglement between two mechanical modes assisted by an optical parametric amplifier (OPA) with a coherent feedback loop. Thus, the hybrid quantum system consists of an optical cavity, an OPA is placed inside, and two charged mechanical oscillators are coupled through a Coulomb force interaction, where the coherent feedback loop is implemented. Following the dynamics of quantum Langevin equations, we employed the quantum Lyapunov continuous variable solution numerically to quantify the macroscopic entanglement through logarithmic negativity. The results show that the presence of OPA, coherent feedback, and robust Coulomb interaction improve the macroscopic entanglement between the two mechanical modes. This phenomenon occurs due to the enhancement of the non-linear gain in the optical parametric amplifier, which leads to an increased number of photons in the cavity. Furthermore, we observe that the state transfer between the spatially separated mechanical oscillators is enhanced with an increase in the intensity of the driving laser. We believe that the present scheme enhances phonon-phonon entanglement transfer through the presence of an OPA and coherent feedback loop and has potential applications in continuous-variable quantum information processing.