Guiding cold atoms in a hollow laser beam

The theory of atom guiding in a far blue-detuned hollow laser beam (HLB) is developed for the dipole interaction scheme described by a three-level $\Lambda$ model. The complete kinetic description of atomic motion based on the Fokker-Planck equation for the atomic distribution function is presented. The dipole gradient force, radiation pressure force, and momentum diffusion tensor are then derived. It is found that even for a far-detuned laser beam, the optical potential for a three-level $\Lambda$ atom is not generally reduced to a sum of two independent potentials associated with the two two-level interactions in the $\Lambda$ scheme. The theory developed here is also compared with the experimental guiding of cold ${}^{85}\mathrm{Rb}$ atoms in the HLB. The experimental results are found to be in good agreement with the Monte Carlo simulations based on the three-level $\Lambda$ model. We observe that the guiding efficiency depends strongly on the intensity and the detuning of the HLB and the initial temperature of atoms. In particular, the experimental results show that, at small detunings, the guiding efficiency is deteriorated strongly by the radiation pressure force. The Monte Carlo simulations also indicate that the efficiency of guiding versus detuning depends strongly on the direction of the HLB propagation with respect to that of atomic motion. Under optimal conditions, the guiding efficiency was found to be about 20%.