Difference between a Photon’s Momentum and an Atom’s Recoil

When an atom absorbs a photon from a laser beam that is not an infinite plane wave, the atom’s recoil is less than $\hslash k$ in the propagation direction. We show that the recoils in the transverse directions produce a lensing of the atomic wave functions, which leads to a frequency shift that is not discrete but varies linearly with the field amplitude and strongly depends on the atomic state detection. The same lensing effect is also important for microwave atomic clocks. The frequency shifts are of the order of the naive recoil shift for the transverse wave vector of the photons.