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

TL;DR

This paper provides a theoretical analysis of micro-motion in a time-averaged orbiting potential trap for condensates, revealing solitary-wave solutions and a natural moving frame of reference, applicable to current experiments.

Contribution

It introduces a novel solitary-wave description of condensate micro-motion in a time-averaged orbiting potential trap, with a systematic approximation of the trap dynamics.

Findings

Existence of solitary-wave solutions in the trap

Identification of a natural moving frame of reference

Validation of the theory for current experimental regimes

Abstract

We present a detailed theoretical analysis of micro-motion in a time-averaged orbiting potential trap. Our treatment is based on the Gross-Pitaevskii equation, with the full time dependent behaviour 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 centre of mass motion in the lab frame. The validity regime for our treatment is carefully defined, and is shown to be satisfied by existing experimental systems.