Motion of cold atoms in far-off-resonant standing wave donut beams

Summary form only given.A donut beam, on the condition of z/spl Lt/z/sub R/ and w(z)/spl sime/w/sub 0/ can be expressed as E(r)=e/sub x/C(r/spl radic/2/w/sub 0/)exp(-r/sup 2//w/sub 2//sup 0/)/spl times/exp[il/spl phi/]exp(ikz), where z/sub R/=/spl pi/w/sub 0//sup 2///spl lambda/, w/sup 2/(z)=/spl pi/(z/sup 2/+z/sub R//sup 2/)//spl lambda//sub R/, r=/spl radic/(x/sup 2/+y/sup 2/), and /spl phi/=arctan(y/x). It has a singularity of phase and the intensity on the axis is zero. For a single donut beam, the scattering force of atoms is related to the phase /spl phi/, which results in azimuthal motion of atoms. In the standing wave donut beams, the scattering force of atoms disappears and the dipole force will be more complicated and related to phase /spl phi/. The motion equations of cold atom in far off-resonant standing wave donut beams are studied theoretically and expressed as dimensionless parameters.