Optical pumping of velocity-selective coherent population trapping states in three-level atoms

An analytical theory of optical pumping of velocity-selective coherent population trapping states in three-level Λ-atoms is presented. The theory is based on an atomic density matrix in the superpositional state representation. The representation introduced for the atomic density matrix directly describes coherent population trapping (CPT) states in a three-level Λ-atom and yields an approximate analytical description for the shape of the two-peak momentum (velocity) distribution of atoms. Optical pumping of velocity-selective CPT states is described in the superpositional state representation as a process of redistribution of atoms in the region of small velocities due to the photon recoil. Typical times of formation of velocity-selective CPT states are found to be inversely proportional to the square of the recoil energy