Fig. 1. Schematic diagram of an achievable double-cavity optomechanical system.

Fig. 2. Fluctuation spectrum as a function of the frequency with different double-cavity coupling coefficient J. The effective detunings of the left cavity mode and right cavity mode and the corresponding decay rates are respectively are ; .

Fig. 3. Optical fluctuation spectrum with different decay rates . The given parameters are ; .

Fig. 4. Optical and atom-optical fluctuation spectrum as a function of the frequency under the influence of parameters. The effective detunings of the left cavity mode and right cavity mode and the corresponding decay rates are respectively are ; . The atomic effective detuning and the coherent decay rates are respectively are . The atom-field coupling strength is . The atomic number is .

Fig. 5. Fluctuation spectrum and atom-optical fluctuation spectrum with given decay rates . The given parameters are , , J = , , ; ,

Fig. 6. Cooling rate as a function of optical coupling coefficient J in the case of different decay rates . The given parameters are , and the optimal detuning satisfied the Eq. (66).

Fig. 7. Mean phonon number as a function of optical coupling coefficient J. The given parameters are , , , , and the optical detuning satisfied the Eq. (66).

Fig. 8. Mean phonon number as a function of effective initial temperature T. The given parameters are , , , , and the optical detuning satisfied the Eq. (66).

Fig. 9. Cooling rate as a function of optical coupling coefficient J. The given parameters are , , , , , , , , , , .

Fig. 10. Mean phonon number as a function of optical coupling coefficient J. The given parameters are same as the ones in Fig. 8.