Unified Master Equation for Molecules in Phonon and Radiation Baths

Abstract

We investigate the dissipative mechanisms of an impurity molecule in crystals using quantum optical master equation. Our unified theory applies generally to polyatomic molecules where several vibrational modes give rise to intramolecular vibrational redistributions. The usual assumption on identical shapes of the nuclear potentials in ground and excited electronic states and the rotating wave approximation have been relaxed, i.e. the vibrational coordinates are different in the ground and excited states, with counter-rotating terms included. Linear vibrational coupling to the lattice phonons accounts for dissipations via non-radiative transitions. The coupling to the electromagnetic field includes Herzberg-Teller interactions in the non-Condon approximation where the transition dipole matrix elements depend on vibrational coordinates. We obtain new cross terms as the result of mixing the terms from the zeroth-order Condon and first-order non-Condon approximations. The corresponding Lamb shifts for all Liouvilleans are derived explicitly including the contributions of counter-rotating terms. The absorption and emission spectra for carbon monoxide computed from our model is in good agreement with experimental data. We show that our unified model is capable of incorporating all typical dissipative relaxation and decoherence mechanisms. The molecular quantum master equation is promising for studies of molecular quantum memory.