Magnon-Photon-Phonon Entanglement in Cavity Magnomechanics

We show how to generate tripartite entanglement in a cavity magnomechanical system which consists of magnons, cavity microwave photons, and phonons. The magnons are embodied by a collective motion of a large number of spins in a macroscopic ferrimagnet, and are driven directly by an electromagnetic field. The cavity photons and magnons are coupled via magnetic dipole interaction, and the magnons and phonons are coupled via magnetostrictive (radiation pressurelike) interaction. We show optimal parameter regimes for achieving the tripartite entanglement where magnons, cavity photons, and phonons are entangled with each other, and we further prove that the steady state of the system is a genuinely tripartite entangled state. The entanglement is robust against temperature. Our results indicate that cavity magnomechanical systems could provide a promising platform for the study of macroscopic quantum phenomena.

Figure 1

(a) Sketch of the system. A YIG sphere is placed inside a microwave cavity near the maximum magnetic field of the cavity mode, and simultaneously in a uniform bias magnetic field, which establish the magnon-photon coupling. The magnon mode is directly driven by a microwave source (not shown) to enhance the magnomechanical coupling. The bias magnetic field ($z$ direction), the drive magnetic field ($y$ direction) and the magnetic field ($x$ direction) of the cavity mode are mutually perpendicular at the site of the YIG sphere. (b) Frequencies and linewidths of the system. The magnon mode with frequency ${\omega }_m$ and linewidth ${\kappa }_m$ is driven by a microwave field at frequency ${\omega }_0$ and the mechanical motion at frequency ${\omega }_b$ scatters photons onto the two sidebands at ${\omega }_0\pm {\omega }_b$. If the magnon mode is resonant with the blue (anti-Stokes) sideband and the cavity with frequency ${\omega }_a$ and linewidth ${\kappa }_a$ is resonant with the red (Stokes) sideband, the system exhibits genuine magnon-photon-phonon entanglement.

Figure 2

Density plot of bipartite entanglement (a) $E_{am}$, (b) $E_{mb}$, and (c) $E_{ab}$ versus detunings ${\mathrm{\Delta }}_a$ and ${\tilde{\mathrm{\Delta }}}_m$. (d) Density plot of $E_{am}$ versus ${\mathrm{\Delta }}_a$ and the ratio of $G_{mb}/g_{ma}$ ($g_{ma}$ is fixed). The parameters are as in (a)–(c) but for ${\tilde{\mathrm{\Delta }}}_m=0.9{\omega }_b$. See text for the details of the other parameters.

Figure 3

(a) $E_{am}$ (dot-dashed), $E_{mb}$ (dashed), and $E_{ab}$ (solid) versus ${\mathrm{\Delta }}_a$, and temperature (see the inset). In the inset ${\mathrm{\Delta }}_a$ is optimized, respectively, for each bipartite entanglement. (b) Tripartite entanglement in terms of the minimum residual contangle ${\mathcal{R}}_{\tau }^{\min }$ versus ${\mathrm{\Delta }}_a$. We take $G_{mb}/2\pi =4.8\mathrm{MHz}$ and ${\tilde{\mathrm{\Delta }}}_m=0.9{\omega }_b$. The other parameters are as in Fig. 2.

Figure 4

(a) $E_{am}$ (dot-dashed), $E_{mb}$ (dashed), and $E_{ab}$ (solid) versus ${\mathrm{\Delta }}_a$. (b) Minimum residual contangle ${\mathcal{R}}_{\tau }^{\min }$ versus ${\mathrm{\Delta }}_a$. The parameters are as in Fig. 3 except for ${\kappa }_a/2\pi =3\mathrm{MHz}$ and ${\kappa }_m={\kappa }_a/5$.