Excitation with Monochromatic Light of a Vibronically Broadened Molecular Band

Abstract

This paper studies the effect of a monochromatic electromagnetic field of arbitrary strength and duration on an isolated molecule presenting the energy level scheme which is the basis for current theories of radiationless processes in the so-called statistical limit: the system is assumed to possess bands of excited levels which are due to the dilution of well separated electric dipole allowed states into a dense set of forbidden states. The frequency of the light is set approximately equal to the transition frequency of one of these bands. Two models are set up, a quantized one with a n-photons one-mode field, and a semiclassical one with an oscillating electric field. They yield identical results. Two limiting cases, termed weak field and strong field can be obtained. In the weak field case, two different steps can be distinguished: first, the excitation of the dipole allowed state; second, the selective excitation of the molecular states at resonance with the field. The strong field case corresponds to a nonlinear response characterized by a damped nutation between ground and allowed states. After a long irradiation time the molecule is left in states which are distributed according to the level scheme corresponding to the ``molecule dressed with photons''. The spontaneous emission rate after the light is switched off is found not to depend on the particular form which is obtained for the initial state. This result, which is shown to hold for more general forms of the electric field in the semiclassical treatment, is a consequence of the analytical properties of the amplitudes.