Conservation laws and laser cooling of atoms

The straightforward application of energy and linear momentum conservation to the absorption/emission of photons by atoms allows us to establish the essential features of laser cooling of two level atoms at low laser intensities. The lowest attainable average kinetic energy of the atoms depends on the ratio {{Γ }}/{E}_{{R}} between the natural linewidth and the recoil energy and tends to E_R as {{Γ }}/{E}_{{R}} tends to zero (in one dimension). This treatment, like the quantum mechanical ones, is valid for any value of the ratio {{Γ }}/{E}_{{R}} and contains the semiclassical theory of laser cooling as the limiting case in which {E}_{{R}}\ll {{Γ }}.