Nonresonant absorption of one photon by one atom and resonant absorption of two photons by two atoms

When a radiation field of frequency ω1 interacts with atoms, etch of which has a transition frequency ωba=(Eb-Ea)/h, with ω1-ωba=Δ≠0, nonresonant absorption can take place with probability P1 inversely proportional to Δ2 (a pressure broadening). When another radiation field of frequency ω2, such that ω1+ω2=2ωba, interacts simultaneously with the gas a resonant two-photon absorption can take place in addition to the nonresonant absorption. The probability of this two-photon absorption process, P2, is found to be inversely proportional to Δ4. If Ω=|| is the Rabi frequency of the transition, it is found that P2/(P1(Δ)+P1(-Δ)) is given by 12 {Ω(-Δ)Ω(-Δ)}2 / {Δ2(Ω(-Δ)2 + Ω(Δ)2)}. (author)