Theory of atomic wave-guidance in dark hollow beam

Nowadays atoms have been guided in the hollow optical fiber[ 11 and blue-detuning dark hollow beam[2], in addition some novel optical traps are constructed by using the dark hollow beam[3][4]. Some theoretical analyses show that the optimal detuning for guiding are in low detuning region[5], they thought there the potential is the highest, but most experimental results show that the optimal detuning were often found in much high detuning region. Until now these differences are not explained in detail. This report is devoted to solve these problems. Firstly the interaction of a three-level A-type atom with a blue-detuning dark hollow beam are described in the dressed-atom picture, the dipole potential and radiation pressure force are derived, the spontaneous emission processes between both adjacent manifolds are analyzed in detail. Then through Monte Carlo simulation, the relations between the guiding efficiency and the detuning in varieties of conditions are acquired. We found that the guiding efficiency also depends on guiding direction relative to the propagation direction of the hollow beam except for the intensity and configuration of the hollow beam and pressure of the chamber, when both directions are opposite, the optimal detuning is in high detuning region, the value is similar to the experimental value. Furthermore we calculated the final velocity distribution of atoms guided by the hollow beam, we found that in same direction case, even though in low detuning region the guiding efficiency is high, but the radial and longitudinal coherence are seriously destroyed, the most atoms are much heated. It is not useful in application to atom optics experiments. The main factors are the radiation pressure forces and photon scattering effects. Finally we found that only in high detuning region the atoms can be guided and their coherence will be held whether same or opposite direction.