Suppression of photon emission from a single molecule by a classical field: Exact analytical solution

The Hamiltonian of a single molecule subjected to laser and classical radio-frequency fields is reduced to that describing a pseudo-spin interacting with vibrational excitations of a semi-classical field. An exact solution is obtained of the Hamiltonian similar to that of an electron linearly interacting with boson excitations, by applying an appropriate unitary operator. The latter gives rise to a coherent 'dressing' of the excited molecule by a large number of semi-classical excitations, which prevents a photon emission by the molecule. The condition of the photon emission suppression is determined by the ratio of the difference of interaction energies of the molecule, in the ground and excited electronic states, with a semi-classical field to the photon energy of radio-frequency field. No full suppression of photon emission occurs when the width Γ of the excited state due to spontaneous emission is finite. For small values of Γ/ω_rf in the range Γ/ ω_rf < 1, the larger the ratio Γ/ω_rf the smaller the suppression of the photon emission, while the suppression practically does not occur for large Γ/ω_rf > 1.