Nonreciprocal photon-phonon entanglement in Kerr-modified spinning cavity magnomechanics

Cavity magnomechanics has shown great potential in studying macroscopic quantum effects, especially for quantum entanglement, which is a key resource for quantum information science. Here we propose to realize magnon mediated nonreciprocal photon-phonon entanglement, which exhibits asymmetry when opposite magnetic or driving fields are respectively applied to the magnons with the Kerr effect or the photons with the Sagnac effect. We find that the mean magnon number can selectively exhibit nonreciprocal linear or nonlinear (bistable) behavior with the strength of the strong driving field on the cavity. Assisted by this driving field, the magnon-phonon coupling is greatly enhanced, leading to the nonreciprocal photon-phonon entanglement via the swapping interaction between the magnons and photons. This nonreciprocal entanglement can be significantly enhanced with the magnon Kerr and Sagnac effects. Given the available parameters, the nonreciprocal photon-phonon entanglement can be preserved at $\approx 3$ K, showing remarkable resilience against the bath temperature. The result reveals that our paper holds promise in developing various nonreciprocal devices with both the magnon Kerr and Sagnac effects in cavity magnomechanics.

Figure 1

(a) Schematic of the Kerr-modified spinning CMM system. $K_0$ is the Kerr coefficient of the magnons, which can be tuned by the direction of the magnetic field $B_0$. When the magnetic field is aligned along the crystal axis $\left[100\right]\left(\right[110\left]\right), K_0>0(<0)$. For the spinning cavity, a positive (negative) frequency shift ${\mathrm{\Delta }}_F$ is produced via the Sagnac effect when the driving field is clockwise (counterclockwise). (b) The coupling configuration. The Kerr magnons with the decay rate ${\kappa }_m$ are coupled to both the photons in the spinning cavity with the decay rate ${\kappa }_a$ and the phonons in the mechanical mode with the decay rate ${\kappa }_b$. The corresponding coupling strengths are $g_{ma}$ and $g_{mb}$.

Figure 2

The mean magnon number vs the normalized amplitude of the driving field with (a) $K_0={\eta }_b{\omega }_b$ and (b) $K_0=0.1{\eta }_b{\omega }_b$, where ${\omega }_b/2\pi =10$ MHz, ${\kappa }_a={\kappa }_m=0.1{\omega }_b, {\kappa }_b/2\pi =100$ Hz, $g_{\mathrm{ma}}=0.2{\omega }_b, g_{mb}={10}^{-3}{\omega }_b, |{\mathrm{\Delta }}_F|=0.2{\omega }_b, {\mathrm{\Delta }}_a=-{\omega }_b$, and ${\mathrm{\Delta }}_m={\omega }_b$.

Figure 3

Density plot of the photon-phonon entanglement $E_{ab}$ as functions of ${\mathrm{\Delta }}_a/{\omega }_b$ and ${\tilde{\mathrm{\Delta }}}_m/{\omega }_b$ with (a) ${\mathrm{\Delta }}_K>0, {\mathrm{\Delta }}_F>0$, (b) ${\mathrm{\Delta }}_K>0, {\mathrm{\Delta }}_F<0$, (c) ${\mathrm{\Delta }}_K<0, {\mathrm{\Delta }}_F>0$, and (d) ${\mathrm{\Delta }}_K<0, {\mathrm{\Delta }}_F<0$. Other parameters are the same as those in Fig. 2 except for $G_{mb}=0.2{\omega }_b, |{\mathrm{\Delta }}_F|=|{\mathrm{\Delta }}_K|=0.1{\omega }_b$, and the bath temperature $T=10$ mK.

Figure 4

The photon-phonon entanglement vs ${\tilde{\mathrm{\Delta }}}_m/{\omega }_b$ with and without the magnon Kerr effect (a, b) and ${\mathrm{\Delta }}_K$ and ${\mathrm{\Delta }}_F$ (c), where (a) ${\mathrm{\Delta }}_F>0$ and (b) ${\mathrm{\Delta }}_F<0$. Other parameters in panels (a)–(c) are the same as those in Fig. 3.

Figure 5

The photon-phonon entanglement vs $G_{mb}/g_{ma}$ with (a) ${\mathrm{\Delta }}_K=0$, (b) ${\mathrm{\Delta }}_K>0$, and (c) ${\mathrm{\Delta }}_K<0$, where the Sagnac effect is considered. (d) The nonreciprocity of the photon-phonon entanglement induced by the magnon Kerr effect vs $G_{mb}/g_{ma}$ with and without the Sagnac effect. Other parameters in panels (a)–(c) are the same as those in Fig. 3.

Figure 6

The photon-phonon entanglement vs ${\kappa }_m/{\kappa }_a$ with (a) ${\mathrm{\Delta }}_K=0$, (b) ${\mathrm{\Delta }}_K>0$, and (c) ${\mathrm{\Delta }}_K<0$, where the Sagnac effect is considered. (d) The nonreciprocity of the photon-phonon entanglement induced by the magnon Kerr effect vs ${\kappa }_m/{\kappa }_a$ with and without the Sagnac effect. Other parameters in panels (a)–(c) are the same as those in Fig. 3.

Figure 7

The photon-phonon entanglement vs the bath temperature $T$ with (a) ${\mathrm{\Delta }}_K=0$, (b) ${\mathrm{\Delta }}_K>0$, and (c) ${\mathrm{\Delta }}_K<0$, where the Sagnac effect is considered. (d) The nonreciprocity of the photon-phonon entanglement induced by the magnon Kerr effect vs $T$ with and without the Sagnac effect. Other parameters in panels (a)–(c) are the same as those in Fig. 3.