Nonreciprocal Bistability in Coupled Nonlinear Cavity Magnonics

TL;DR

The paper presents a coupled nonlinear cavity–magnon system incorporating a Kerr-magnon YIG sphere to achieve tunable nonreciprocity in magnonic transport. It derives a critical impedance-matching condition for reciprocity in the absence of magnon driving and shows that Kerr nonlinearity shifts this condition to a controllable pair (J_c, λ_c). Numerical results demonstrate strong, tunable nonreciprocity by detuning inter-cavity coupling J and parametric strength λ, and reveal that a magnon-driving field can induce pronounced nonreciprocity even when the condition is unbroken. The work offers a versatile platform for highly tunable nonreciprocal devices in nonlinear cavity magnonics, with potential impact on quantum information processing and networks.

Abstract

We propose a coupled nonlinear cavity-magnon system, consisting of two cavities, a second-order nonlinear element, and a yttrium-iron-garnet (YIG) sphere that supports Kerr magnons, to realize the sought-after highly tunable nonreciprocity. We first derive the critical condition for switching between reciprocity and nonreciprocity in the absence of magnon driving, and then numerically demonstrate that strong magnonic nonreciprocity can be achieved by violating this critical condition. When magnons are driven, we show that strong magnonic nonreciprocity can also be attained even within the critical condition. Compared to previous studies, the introduced nonlinear element not only relaxes the critical condition in both the weak and strong coupling regimes, but also offers an alternative means to tune magnonic nonreciprocity. Our work provides a promising avenue for realizing highly tunable nonreciprocal devices based on Kerr magnons.

Figures (9)

• Figure 1: Schematic diagram of the coupled nonlinear cavity magnonics. The system is composed of a PDC coupled to a MC embedded a YIG sphere with coupling strength $J$. The PDC can be realized by placing a second-order nonlinear element in a cavity. $g$ is the photon-magnon coupling strength, $\lambda$ is the parametric strength of the nonlinear element, $\omega_p$ is the frequency of the pumping field on the nonlinear element, $\Omega_1$, $\Omega_2$, and $\Omega_m$ are three resonant driving fields. We here assume that the crystallographic axis of the YIG sphere is along the $z$-direction.
• Figure 2: The scaled magnon number as a function of the input power ($P_1=P_2=P$) of the driving field on the PDC (MC) with the critical condition in Eq. (\ref{['eq20']}) (a) unbroken and (b, c, d) broken, where (a) $J=J_c$ and $\lambda=\lambda_c$, (b) $J=0.8J_c$ and $\lambda=\lambda_c$, (c) $J=J_c$ and $\lambda=0.2\lambda_c$, and (d) $J=0.8J_c$ and $\lambda=0.2\lambda_c$. The red solid (blue dashed) curve denotes the magnon number when the PDC (MC) is driven. Other parameters are chosen as: $\eta_1=\eta_2=\eta_m=0.5$, $\omega_m/2\pi=\omega_d/2\pi=10.1$ GHz, $g/2\pi=41$ MHz, $\gamma_m/2\pi=20$ MHz, $\kappa_1/2\pi=5\kappa_2/2\pi=25$ MHz, $\Delta_1=\Delta_2=4\gamma_m$, $\Delta_m=\omega_m-\omega_d$, $K/2\pi=0.5$$\mu$Hz, and $P_m=0$.
• Figure 3: The scaled magnon number as a function of the frequency detuning ($\Delta_1=\Delta_2=\Delta$) of the PDC (MC) from the driving field with the critical condition in Eq. (\ref{['eq20']}) (a) unbroken and (b,c,d) broken, where (a) $J=J_c$ and $\lambda=\lambda_c$, (b) $J=0.8J_c$ and $\lambda=\lambda_c$, (c) $J=J_c$ and $\lambda=0.2\lambda_c$, and (d) $J=0.8J_c$ and $\lambda=0.2\lambda_c$. The red solid (blue dashed) curve denotes the magnon number when the PDC (MC) is driven. Other parameters are the same as those in Fig. \ref{['fig2']} except for $P_1=P_2=P=100$ mW, $\Delta_m=\Delta_1=\Delta_2=\Delta$, and $\omega_d=\omega_m-\Delta$.
• Figure 4: The scaled magnon number as a function of the biased magnetic field ($H=\omega_m/\gamma$) with the critical condition in Eq. (\ref{['eq20']}) (a) unbroken and (b,c,d) broken, where (a) $J=J_c$ and $\lambda=\lambda_c$, (b) $J=0.8J_c$ and $\lambda=\lambda_c$, (c) $J=J_c$ and $\lambda=0.2\lambda_c$, and (d) $J=0.8J_c$ and $\lambda=0.2\lambda_c$. The red solid (blue dashed) curve denotes the magnon number when the PDC (MC) is driven. Other parameters are the same as those in Fig. \ref{['fig2']} except for $P_1=P_2=P=100$ mW and $\Delta_1=\Delta_2=\Delta=0.1\gamma_m$.
• Figure 5: The scaled magnon number as a function of the Kerr coefficient ($K$) with the critical condition in Eq. (\ref{['eq20']}) (a) unbroken and (b,c,d) broken, where (a) $J=J_c$ and $\lambda=\lambda_c$, (b) $J=0.8J_c$ and $\lambda=\lambda_c$, (c) $J=J_c$ and $\lambda=0.2\lambda_c$, and (d) $J=0.8J_c$ and $\lambda=0.2\lambda_c$. The red solid (blue dashed) curve denotes the magnon number when the PDC (MC) is driven. Other parameters are the same as those in Fig. \ref{['fig2']} except for $P_1=P_2=P=100$ mW and $\Delta_1=\Delta_2=\Delta=\gamma_m$.