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.
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