Phase-switchable nonreciprocal entanglement via magnon squeezing in ring-cavity optomagnomechanics

Cavity optomagnomechanics provides a versatile platform to explore macroscopic quantum correlations, particularly nonreciprocal entanglement. In this work, we propose a theoretical scheme to generate switchable bipartite and tripartite entanglement in an optomagnomechanical ring cavity by exploiting phase-controlled magnon squeezing. Indeed, two spatially separated ferrimagnetic YIG microbridges become entangled through their magnetostriction-mediated coupling to mechanical motion and a common cavity field via radiation-pressure interaction. The squeezing process introduces two phase-dependent contributions to the magnon response, namely an effective detuning shift $\Delta_{\theta_j}$ and a quadrature-damping contribution $\kappa_{\theta_j}$, both of which reverse sign upon a $\pi$ phase shift, providing an in situ control to switch the entanglement response. The nonreciprocal entanglement is defined operationally through the asymmetric entanglement response under the phase reversal $\theta_j \to \theta_j + \pi$, quantified by normalized contrast ratios $C_E$ and $C_{\mathcal{R}}$, which measure the relative difference between the entanglement obtained at $\theta_j$ and at the phase-reversed configuration $\theta_j+\pi$. The resulting phase-tuning method provides a flexible and robust route to achieve high-contrast bipartite and tripartite entanglement within stable parameter regions, establishing magnon squeezing as a practical quantum resource for switchable quantum correlations in hybrid platforms.