Laser Cooling of Atomic Beams and its Application to Frequency Standards

Abstract

When an atom absorbs or emits a photon, the momentum conservation law implies that its momentum must change by a quantity equal to the photon momentum hv/c. Let us consider an atom irradiated by a running wave, resonant with an atomic transition. Each absorption-spontaneous emission cycle will lead to a variation of the atom velocity of a quantity hv/mc. At contrary, an absorption followed by a stimulated emission process, with two equal photons, does not change the atomic momentum. Thus, taking into account also the saturation effects, an atom experiences an effective force given by the ratio of the photon momentum with the mean time interval between two spontaneous emission, that is

$$F = \frac{{h\gamma }} {\lambda }\frac{S} {{1 + S + (\Delta \omega - kv)^2 /\gamma ^2 }}$$

(1)

where γ is the HWHM homogeneous linewidth, λ=c/ν is the resonance wavelength, and S=I/Is the saturation parameter of the radiation.