We investigate the interplay between photonic and phononic spectral dynamics in a cavity optomechanical system driven by radiation pressure coupling. Employing a semi-classical Hamiltonian framework, we derive the quantum Langevin equations governing the photon and phonon mode fluctuations, enabling explicit calculation of their noise spectra. The system comprises a high-finesse optical microcavity with a movable mirror acting as a mechanical oscillator, irradiated by a red-detuned 1064-nm laser. As the optomechanical coupling strength G increases to its maximum \(G_m\) , the photon noise spectrum \(S_a(\omega )\) exhibits significant amplification and broadening, accompanied by a suppression and frequency shift in the phonon spectrum \(S_q(\omega )\) . This reciprocal behavior confirms energy transfer from the mechanical to the optical mode, consistent with laser cooling principles. Our analysis reveals that the effective mechanical frequency \(\omega _{eff}\) and damping rate \(\gamma _{eff}\) are renormalized under enhanced optomechanical coupling, leading to spectral imbalance and cooling rates proportional to \(S_q(\omega )-S_q(-\omega )\) . Notably, the mechanical mode’s effective temperature is reduced by several orders of magnitude, demonstrating sub-millikelvin cooling capabilities. These results highlight the critical role of coupling strength in optimizing cooling efficiency and photon-mediated control, with implications for quantum metrology, state engineering, and noise suppression in hybrid quantum systems.
