Fig. 1. Diagram of eigen-energy levels of mixed cavity optomechanical system in zero-, one-, and two-photon subspaces

Fig. 2. Two-photon scattering spectrum S(Δ_p,Δ_q)ωM2 as a function of photon frequency detunings Δ_p/ω_M and Δ_q/ω_M for different coupling strengths when initial mechanical ground state is |0>_b. (a) g₁/ω_M=0.20, g₂/ω_M=0.08; (b) g₁/ω_M=0.20, g₂/ω_M=0.01; (c) g₁/ω_M=0.40, g₂/ω_M=0.01; (d) zoomed view of peak with center position Δ_p+Δ_q=-δ in Fig. 2(c)

Fig. 3. Two-photon scattering spectra S(Δ_p,Δ_q)ωM2 as functions of Δ_p/ω_M and Δ_q/ω_M for various values of coupling strength g₂when the mechanical mode is in the ground state |0>_b. (a)-(c) Corresponding to g₂/ω_M=0.01, 0.05, 0.10, respectively; (d)-(f) joint spectra S(Δ,Δ)ωM2 along diagonal line Δ_p=Δ_q=Δ in corresponding to Figs. 3(a)-(c)

Fig. 4. Two-photon scattering spectra S(Δ,Δ)ωM2 along diagonal line Δ_p=Δ_q=Δ for different coupling strength g₁. (a) g₁/ω_M=0.01; (b) g₁/ω_M=0.10; (c) g₁/ω_M=0.50

Fig. 5. Two-photon scattering spectra S(Δ,Δ)ωM2 along diagonal line Δ_p=Δ_q=Δ at various values of γ_c. (a) γ_c/ω_M=0.01; (b) γ_c/ω_M=0.10; (c) γ_c/ω_M=0.80