Atom trapping and dynamics in the interaction of optical vortices with quadrupole-active transitions

Recent studies have confirmed the coupling of optical vortices, such as Laguerre-Gaussian and Bessel-Gaussian modes, to quadrupole-active atomic transitions. This interaction has been shown to be enhanced considerably in the case of Laguerre-Gaussian beams due to the gradient coupling, particularly in the case of a relatively large winding number. Here we consider the trapping and the dynamics of atoms in the optical quadrupole potential generated by two co-axial counter-propagating optical vortex beams. We focus on the atomic transition $6^2S_{1/2}\rightarrow 5^2D_{5/2}$ in Cs which is a dipole-forbidden, but a quadrupole-allowed transition. We show how this atomic transition engages with the optical vortex fields at near-resonance, leading to atom trapping in the optical quadrupole potential well accompanied by translational motion. We set out the formalism leading to atom trapping and show how the optical forces generate the atomic motion, illustrating the results using typical experimentally accessible parameters.