Atoms in axially shifted tightly focused counter-propagating beams:The role of the Gouy and curvature phases

We consider the interaction of atoms with two tightly focused and axially shifted counter-propagating optical beams. At sub-wavelength focusing, we find that the scattering force potential in the three-dimensional space between the shifted focal planes changes from a feature with a saddle-point to a three-dimensional trapping potential. Further analysis shows that due to the tight focusing, the trapping depends on significant contributions arising from the Gouy and curvature phase gradients of the interfering beams. The physics and its effects are illustrated with reference to the sub-wavelength trapping of sodium atoms.