Theory of electronic-state coherences produced in radiatively-aided inelastic collisions

In a previous paper [P. R. Berman and E. Giacobino, Phys. Rev. A 28, 2900 (1983)], a method was proposed for producing electronic-state coherences using radiatively-aided inelastic collisions (RAIC). Two atoms collide in the presence of two simultaneously applied laser pulses and the combined action of the fields and the collision leads to a final-state coherence ${\rho }_{\mathrm{ij}}$ between levels $i$ and $j$ in one of the atoms. In this paper a detailed calculation of the RAIC cross section is given, including effects of magnetic degeneracy and an average over all collision orientations. With an isotropic distribution of collision orientations and with one photon absorbed from each laser field in a single RAIC reaction, a final-state coherence ${\rho }_{\mathrm{ij}}$ is created only if states $i$ and $j$ have the same parity. In order to produce a final-state coherence between states of opposite parity, an anisotropic distribution of collision orientations is needed. Estimates of RAIC cross sections are obtained for both isotropic and axially symmetric distributions of collision orientations. For final states having opposite parity, the RAIC reaction can lead to the production of coherent radiation at the sum or difference frequency of the applied laser fields.