Fig. 1. Diagram of the hybrid system and its physical model. (a) Diagram of the hybrid device of the nonreciprocal quantum interface between the acoustic cavity and the optical cavity mediated by mechanical resonator. (b) The physical model diagram of nonreciprocal information transfer and its two-channel interference. (${\mathit{T}}_{\mathrm{31}}$ channel acoustic signal passes through the surface acoustic cavity through the mechanical oscillator to the optical cavity, namely a→b→c; the ${\mathit{T}}_{\mathrm{13}}$ channel contains two coherent paths, namely ① c→b→a and ② c→d→b→a. The ${\mathit{T}}_{\mathrm{21}}$ channel path is $\mathrm{a}\to \mathrm{b}$. The ${\mathit{T}}_{\mathrm{32}}$ channel path is $\mathrm{b}\to \mathrm{c}.$ The ${\mathit{T}}_{\mathrm{43}}$channel path is $\mathrm{c}\to \mathrm{d}$. The${\mathit{T}}_{\mathrm{14}}$ channel path is $\mathrm{d}\to \mathrm{a}$. )

Fig. 2. When $G_a/\mathrm{2}\mathrm{\pi }\in [-\mathrm{100,100}]$ MHz, $G_c/\mathrm{2}\mathrm{\pi }\in [-\mathrm{100,100}]$ MHz, ${\gamma }_m/\mathrm{2}\mathrm{\pi }=\mathrm{0.01}$ MHz, ${\kappa }_{a,c}/\mathrm{2}\mathrm{\pi }=\mathrm{10}$ MHz, the three-dimensional change diagram of${\mathit{T}}_{\mathrm{31}}$varying with $G_a$ and ${\mathrm{G}}_c$

Fig. 3. When $G_c/\mathrm{2}\mathrm{\pi }\in [-\mathrm{100,100}]$ MHz, the function curves of $T_{\mathrm{31}}$varying with $G_{\mathrm{c}}$ with different parameters $G_a$ and ${\gamma }_m$

Fig. 4. When ${\mathrm{G}}_c/\mathrm{2}\mathrm{\pi }\in [-\mathrm{100,100}]$ MHz, the function curve of ${\left|{\mathit{T}}_{\mathrm{31}}\right|}^{\mathrm{2}}$ versus the coupling constant $G_c$