Collimation and compression of atomic beams under conditions of coherent population trapping

A theoretical investigation was made of the collimation and compression of atomic beams under two-frequency cooling conditions. It was possible to reach cooled atom temperatures right down to $T_R=\hslash^2k/2Mk_B\approx10^{-6}$ K, determined by the recoil energy of the atom. The dependences of the temperature on the frequency difference between the light waves were investigated, for velocities near zero, and these were found to be in qualitative agreement with those observed experimentally. An expression for the beam diameter after compression by diverging waves was derived. Estimates of these effects are given for cases of practical importance.