Rabi oscillations in the scattering-state representation.

Abstract

This paper presents an analysis of the Rabi oscillations of two-level atoms in the scattering-state representation. A collision complex obtained from a pair of identical two-level atoms is coupled to a field mode and it is found that there can be three distinct Rabi frequencies. These reduce to a single Rabi frequency for a photon distribution that is sharply peaked around an average number n\ifmmode\bar\else\textasciimacron\fi{}\ensuremath{\gg}1. One then finds that, in addition to the three frequency components in the off-diagonal element of the atomic density matrix, there are two components that are symmetrically displaced around the mode frequency at intervals of twice the Rabi frequency. They represent the collisionally induced cooperative motion of the atoms. When various observable quantities are averaged over the orientation of the complex, one obtains results that apply to many-atom systems in the binary collision approximation. Collisional effects do not enter the above results as lifetimes due to the fact that scattering states have precisely defined energies and correspond to entire particle histories. The collision potential opens up new radiative coupling channels, which collectively represent spectral line broadening. The collision potential and the radiative coupling combine to produce static and quasistatic dipole moments for the complex. At the threshold for atomic population inversion, the density matrix for the complex, as well as for an atom, becomes a constant multiple of the identity matrix, demonstrating that the threshold of stimulated emission is also a critical point for collisional effects, within the approximations of this paper.