Nonreciprocal entanglement in cavity magnomechanics exploiting chiral cavity-magnon coupling

TL;DR

The paper addresses generating nonreciprocal quantum entanglement in a cavity magnomechanical system by exploiting chiral cavity-magnon coupling in a torus-shaped cavity, which hosts two degenerate counter-propagating modes $a_{\circlearrowright}$ and $a_{\circlearrowleft}$ along with a magnon mode $m$ and mechanical mode $q,p$. By linearizing the dynamics under a strong drive, the authors derive quantum Langevin equations $\dot{u}(t)=A u(t)+n(t)$ and compute the steady-state covariance matrix $V$ by solving the Lyapunov equation $A V+V A^T=-D$, from which the logarithmic negativity $E_N=\max[0,-\ln(2\eta^-)]$ quantifies entanglement. In the ideal case, CW driving yields microwave-magnon and microwave-phonon entanglement and a photon-magnon-phonon tripartite entanglement, while CCW driving fails to produce such entanglement due to the chiral coupling $g_{\circlearrowright} \gg g_{\circlearrowleft}$. The authors demonstrate robustness to imperfections (e.g., backscattering $J$, residual $g_{\circlearrowleft}$) and thermal noise, and they propose a channel-multiplexing quantum teleportation protocol with fidelity $\mathcal{F}=1/\sqrt{\det V}$ achieving around $0.55$ in their parameter regime, suggesting applications in noise-tolerant quantum processing and chiral magnonic networks.

Abstract

We propose a new mechanism to achieve nonreciprocal quantum entanglement in a cavity magnomechanical system by exploiting the chiral cavity-magnon coupling. The system consists of a magnon mode, a mechanical vibration mode, and two degenerate counter-propagating microwave cavity modes in a torus-shaped cavity. We show that nonreciprocal stationary microwave-magnon and -phonon bipartite entanglements and photon-magnon-phonon tripartite entanglement can be achieved by respectively driving different circulating cavity modes that hold a chiral coupling to the magnon mode. The nonreciprocal entanglements are shown to be robust against various experimental imperfections. We specifically show how such nonreciprocal entanglement can realize the channel multiplexing quantum teleportation from a microwave field to a solid-state magnon mode. The work may find promising applications of the cavity magnomechanical systems in noise-tolerant quantum processing, channel multiplexing quantum teleportation, and chiral magnonic quantum networks.

Figures (8)

• Figure 1: (a) Schematic diagram of the CMM system based on a torus-shaped microwave cavity. The CW (CCW) circulating microwave cavity mode is driven by an external microwave field at frequency $\omega_0$ via a waveguide. $\hat{r}$ ($\hat{k}$) denotes the unit vector of the polar ($z$) axis. (b) Frequencies and linewidths of the system. Due to the chiral coupling between magnons and CW (CCW) propagating microwave photons, nonreciprocal microwave-magnon and -phonon bipartite entanglements and photon-magnon-phonon tripartite entanglement are generated when the cavity (magnon) mode is resonant with the Stokes (anti-Stokes) sideband scattered by the mechanical motion.
• Figure 2: Density plot of the entanglement (a) $E_{a_{\circlearrowright}m}$ and (b) $E_{a_{\circlearrowright}b}$ versus detunings $\Delta_a$ and $\tilde{\Delta}_m$. (c) Density plot of $E_{a_{\circlearrowright}b}$ versus cavity decay rate $\kappa_a$ and drive power $P_0$ at optimal detunings $\Delta_a=-0.76\omega_b$ and $\tilde{\Delta}_m=0.65\omega_b$. $\kappa_{a,i}$ is fixed in varying $\kappa_a$. The other parameters are the same as in (b). (d) Microwave-magnon entanglement $E_{a_{\circlearrowright}m}$ (dashed) and microwave-phonon entanglement $E_{a_{\circlearrowright}b}$ (solid) versus mechanical damping rate $\gamma_b$. The parameters used for plotting $E_{a_{\circlearrowright}m}$ ($E_{a_{\circlearrowright}b}$) are as the same in (a) [(b)] but at optimal detunings $\Delta_a=-0.72\omega_b$ and $\tilde{\Delta}_m=0.76\omega_b$ ($\Delta_a=-0.76\omega_b$ and $\tilde{\Delta}_m=0.65\omega_b$). See text for the other parameters.
• Figure 3: (a) [(b)]Tripartite entanglement in terms of the minimum residual contangle $R_{a_{\circlearrowright}mb}$ versus $\Delta_a$, with the paramters as used in plotting of Fig. \ref{['fig2']}(a) [Fig. \ref{['fig2']}(b)] and $\tilde{\Delta}_m=0.76\omega_b$ ($0.65\omega_b$).
• Figure 4: Stationary entanglement $E_{a_{\circlearrowright}\nu}^{(\circlearrowright)}$ (thick solid), $E_{a_{\circlearrowleft}\nu}^{(\circlearrowright)}$ (thin solid), $E_{a_{\circlearrowright}\nu}^{(\circlearrowleft)}$ (thick dashed) and $E_{a_{\circlearrowleft}\nu}^{(\circlearrowleft)}$ (thin dashed) versus coupling strength $J$ under $\chi \equiv g_\circlearrowleft^{ }/g_\circlearrowright^{ }=0.1$ in (a)-(b); versus $\chi$ under $J=0.5\kappa_m$ in (c) and $J=\kappa_m$ in (d). Here, the subscript $\nu=m$ in (a) and (c) for microwave-magnon entanglement; $\nu=b$ in (b) and (d) for microwave-phonon entanglement. The superscript ($\circlearrowright$) or ($\circlearrowleft$) denotes the specific circulating mode under drive. The drive power used in (a) and (c) [(b) and (d)] corresponds to the value of $|G_m|$ used for $E_{a_{\circlearrowright}m}$ ($E_{a_{\circlearrowright}b}$) in Fig. \ref{['fig2']}(d). We take $\gamma_b/2\pi=10^2$ Hz, and the other parameters in (a) and (c) [(b) and (d)] are the same as those used to obtain $E_{a_{\circlearrowright}m}$ ($E_{a_{\circlearrowright}b}$) in Fig. \ref{['fig2']}(d).
• Figure 5: Stationary entanglement $E_{a_{\circlearrowright}\nu}^{(\circlearrowright)}$ (thick solid), $E_{a_{\circlearrowleft}\nu}^{(\circlearrowright)}$ (thin solid), $E_{a_{\circlearrowright}\nu}^{(\circlearrowleft)}$ (thick dashed) and $E_{a_{\circlearrowleft}\nu}^{(\circlearrowleft)}$ (thin dashed) versus bath temperature $T$. Here, $\nu=m$ in (a) for microwave-magnon entanglement; $\nu=b$ in (b) for microwave-phonon entanglement. We take $\chi=0.1$ and the other parameters of (a) and (b) are the same as in Figs. \ref{['fig4']}(c) and \ref{['fig4']}(d), respectively.