Enhancement of magnon-photon-phonon entanglement in a cavity magnomechanics with coherent feedback loop

In this paper, we present a coherent feedback loop scheme to enhance the magnon-photon-phonon entanglement in cavity magnomechanics. We provide a proof that the steady state and dynamical state of the system form a genuine tripartite entanglement state. To quantify the entanglement in the bipartite subsystem and the genuine tripartite entanglement, we use the logarithmic negativity and the minimum residual contangle, respectively, in both the steady and dynamical regimes. We demonstrate the feasibility of our proposal by implementing it with experimentally realizable parameters to achieve the tripartite entanglement. We also show that the entanglement can be significantly improved with coherent feedback by appropriately tuning the reflective parameter of the beam splitter and that it is resistant to environmental thermalization. Our findings pave the way for enhancing entanglement in magnon-photon-phonon systems and may have potential applications in quantum information.