Fig. 1. Schematic diagram of double-Laguerre-Gaussian-cavity optomechanical system coupling with nonlinear OPA medium^[33-35]

Fig. 2. Optical force noise spectrum SFFω as a function of ω/ωϕ

Fig. 3. Optical force noise spectrum SFFω as a function of ω/ωϕ. (a) SFFω in coupled cavity condition; (b) SFFω in single cavity condition

Fig. 4. SFFω as a function of ω/ωϕ for four different detuning Δc1

Fig. 5. Optical force noise spectrum SFFω as a function of ω/ωϕ and net cooling rate Γ as a function of decay rate κ2/ωϕ. (a) Optical force noise spectrum SFFω as a function of ω/ωϕ with three different decay rates κ2 of auxiliary cavity; (b) net cooling rate Γ as a function of decay rate κ2/ωϕ of auxiliary cavity

Fig. 6. Net cooling rate Γ as a function of coupling strength J/ωϕ

Fig. 7. Final phonon number nf as a function of coupling strength J/ωϕ

Fig. 8. Final phonon number nf as a function of detuning Δc1/ωϕ and Δc2/ωϕ

Fig. 9. Final phonon number nf as a function of initial phonon number nth and cavity field decay rate κ1/ωϕ