in Fig. S-1(b) are plotted in Fig. S-2; they respectively become stable oscillations together with the cavity photon numbers and thermal phonon numbers. Such stable oscillation looks similar to those of classical OMSs due to the saturated nonlinear effect in the blue-detuned regime (see Sec. VIII in [@rev]), but has a different physical origin from that type of classical motion since we are currently concerned with the red-detuned regime. Another interesting phenomenon in the processes is the considerably increased average cavity photon numbers from that of an uncoupled system, when the systems become stabilized. We illustrate its mechanism in Fig. S-1(c), which shows that the increased photon numbers in cavity is due to the constructive interference of two factors, the displacement term irrelevant to the optomechanical coupling \[the first term, which is from the unitary action $U_0(t)$, inside the absolute sign in Eq. (\[c3\])\] and the cavity mode amplitude induced by the optomechanical coupling (the summation of the rest terms, which come from the coherent drive term $\vec{\lambda}(t)$ in Eq. (\[dynamics\]), in the same equation). The latter can be regarded as a relatively small effect for a weakly coupled OMS. Such constructive interference, which is predicted with a completely quantum 