  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 show how the optical forces generate the motion of the
atoms trapped within the quadrupole potential, illustrating the results using
typical experimentally accessible parameters.
