Stimulated Raman transition ($\Delta E=\hslash ({\omega }_1-{\omega }_2),\Delta \mathbf{p}=\hslash ({\mathbf{k}}_1-{\mathbf{k}}_2)$)

Coherent absorption from one applied beam and stimulated emission into another, transferring an atom between two long-lived states. The energy transfer uses the frequency difference and the momentum transfer the wavevector difference. It is distinct from an absorption-absorption process.

Eliminating a common far-detuned intermediate state with single-photon couplings $\hslash {\Omega }_1/2$ and $\hslash {\Omega }_2/2$ gives effective Rabi angular frequency of magnitude $|{\Omega }_1{\Omega }_2|/(2|\Delta |)$. The complex laser phases set the coupling phase, and differential AC Stark shifts change the two-photon resonance.