  We consider the Molecular Opto-mechanical systems in back-action
amplification of single molecule Raman imaging. Surface Enhanced Raman
Scattering (SERS) is mapped into the dissipative cavity opto-mechanics system
of coupled resonators. We investigate the plasmon molecular vibration
interactions in strong coupling regimes of cavity opto-mechanics in the
presence of impurities. Eigenfunction spectrum is analyzed for the normal mode
splitting of photonic and mechanical hybrid system. Back-action transduction of
photons into mechanical modes is investigated by avoided crossing due to the
nonlinear interactions and Casimir forces in the presence of virtual photons
and radiation pressure. In input-output coupled cavity scheme, both cavity and
driving fields are analyzed for the absorption and dissipation of heat in weak
and strong coupling regimes of the cascaded cavity setup. In terms of the
second order coherence functions, thermodynamic work and heat engine are
investigated via phonon lasing of mechanical mode in opto-mechanical
implementation of Brownian motors by tuning the competing coupling strengths of
impurities and nonlinearities.
