Solitary-wave description of condensate micromotion in a time-averaged orbiting potential trap

We present a detailed theoretical analysis of micromotion in a time-averaged orbiting potential trap. Our treatment is based on the Gross-Pitaevskii equation, with the full time-dependent behavior of the trap systematically approximated to reduce the trapping potential to its dominant terms. We show that within some well specified approximations, the dynamic trap has solitary-wave solutions, and we identify a moving frame of reference which provides the most natural description of the system. In that frame eigenstates of the time-averaged orbiting potential trap can be found, all of which must be solitary-wave solutions with identical, circular center of mass motion in the laboratory frame. The validity regime for our treatment is carefully defined, and is shown to be satisfied by existing experimental systems.