Line shape and atomic efficiency of two-photon absorption using counter-propagating beams to reduce Doppler effects

Doppler effects can be reduced or eliminated for two-photon absorption if the atoms are made to absorb one photon from each of two counter-propagating beams. We derive the line shape for the transition as a function of the frequency difference of the two beams and specifically consider the variation of the linewidth and of the efficiency of utilization of the available atoms.