Hybrid Cavity-Magnon Optomechanics: Tailoring Bipartite and Tripartite Macroscopic Entanglement

TL;DR

The paper addresses generating tunable macroscopic entanglement in a hybrid cavity-magnon optomechanical system by embedding magnons in a driven cavity that interacts with a mechanical mode. By linearizing the dynamics and solving a Lyapunov equation for the covariance matrix, it quantifies bipartite and tripartite entanglement using logarithmic negativity and minimal residual contangle within a Gaussian-state framework. Key findings show that magnon-photon coupling and detunings can optimize optomechanical, magnon-magnon, and several tripartite entanglements, with robustness to bath temperature up to a survival threshold and interesting role of magnon decay in protecting certain correlations. The work outlines feasible experimental implementations with current microwave optomechanics and YIG-sphere technology and suggests practical paths to tunable macroscopic quantum correlations in hybrid systems for quantum information processing and fundamental tests.

Abstract

Cavity optomechanics, providing an inherently nonlinear interaction between photons and phonons, have shown enomerous potential in generating macroscopic quantum entanglement. Here we propose to realize diverse bipartite and tripartite entanglement in cavity-magnon optomechanics. By introducing magnons to standard cavity optomechanics, not only tunable optomechanical entanglement and magnon-magnon entanglement can be achieved, but also flexible tripartite entanglement including magnon-photon-phonon entanglement, magnon-magnon-photon and -phonon entanglement can be generated. Moreover, optimal bipartite and tripartite entanglement can be achieved by tuning parameters. We further show that all entanglement can be enhanced via engineering the magnon-photon coupling, and is proven to be robust against the bath temperature within the survival temperature. Besides, we find that the optomechanical entanglement can be protected or restored by bad magnons with large decay rate, while other entanglement is severely reduced. The results indicate that our proposal provides a novel avenue to explore and control tunable macroscopic quantum effects in hybrid cavity-magnon optomechanics.

Figures (8)

• Figure 1: (a) Schematic diagram of the proposed cavity-magnon optomechanics. It consists of two YIG spheres placed in biased magnetic field $B_0$, a driven cavity and a mechanical resonator. The cavity mode is strongly coupled to the Kittle modes of two YIG spheres, and weakly coupled to the mechanical mode. (b) The effective coupling configuration. $G$ is the linearized optomechanical coupling strength, and $g_{1(2)}$ is the tunable coupling strength between the cavity mode and the Kittle mode of the YIG sphere $1~(2)$.
• Figure 2: (a) The optomechanical entanglement ($E_N^{ab}$) vs the dimensionless normalized cavity detuning $\tilde{\Delta}_a/\omega_b$ with different optomechanical coupling strengths $G/\kappa_a=1,3,5$ at the bath temperature $T=20$ mK, where $\tilde{\Delta}_a$ is the cavity detuning and $\omega_b$ is the frequency of the mechanical mode. (b) The LN $E_N^{ab}$ vs the bath temperature $T$ with the moderate optomechanical coupling strength $G/\kappa_a=4$ and the frequency detuning $\tilde{\Delta}_a=0.9\omega_b$. Other parameters are chosen as $\omega_a/2\pi=10$ GHz, $\omega_b/2\pi=10$ MHz, $\kappa_a/2\pi=1$ MHz, $\gamma_b/2\pi=100$ Hz.
• Figure 3: Density plot of $E_N^{ab}$ vs the normalized frequency detuning $\Delta_m/\omega_b$ and the normalized magnon-photon coupling strength $g_m/G$ with (a) $\kappa_m=\kappa_a$ and (b) $\kappa_m=10\kappa_a$. (c) The optomechanical entanglement ($E_N^{ab}$), the magnon-photon entanglement ($E_N^{am}$), and the magnon-phonon entanglement ($E_N^{bm}$), vs the normalized magnon frequency detuning $\Delta_m/\omega_b$, where $g_m=G$ and $\kappa_m=2\kappa_a$. (d) The optomechanical entanglement vs the normalized frequency detuning $\Delta_m/\omega_b$ with different values of $\kappa_m/\kappa_a=2,5,10$. The star means the optimal entanglement. (e) The magnon-photon-phonon entanglement ($\mathcal{R}_\tau^{abm}$) vs the normalized magnon frequency detuning $\Delta_m/\omega_b$ with different magnon-photon coupling strengths $g_m/G=0.2,0.6,1$, where $\kappa_m=\kappa_a$ is taken. Other parameters are the same as those in Fig. \ref{['fig2']}(a) except for $G=4\kappa_a$ and $\tilde{\Delta}_a=0.9\omega_b$.
• Figure 4: Density plot of the magnon-magnon entanglement ($E_N^{m_1m_2}$) vs the normalized magnon frequency detunings $\Delta_1/\omega_b$ and $\Delta_2/\omega_b$ with (a) $\kappa_m=\kappa_a$ and (b) $\kappa_m=2\kappa_m$. Other parameters are the same as those in Fig. \ref{['fig2']}(a) except for $g_m=G=4\kappa_a$ and $\tilde{\Delta}_a=0.9\omega_b$.
• Figure 5: (a) Density plot of the magnon-magnon entanglement ($E_N^{m_1m_2}$) vs the normalized magnon-photon coupling strengths $g_1/G$ and $g_2/G$. (b) The optomechanical entanglement ($E_N^{ab}$) and the magnon-magnon entanglement ($E_N^{m_1m_2}$) vs the normalized magnon-photon coupling strength $g_m/G$. Other parameters are the same as those in Fig. \ref{['fig2']}(a) except for $\Delta_1=-\omega_b$, $\Delta_2=\omega_b$, $\kappa_m=\kappa_a$, $G=4\kappa_a$ and $\tilde{\Delta}_a=0.9\omega_b$.