有哪些信誉好的足球投注网站Solitary-wave description of condensate micro-motion in a time-averaged orbiting potential.pdf
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Solitary-wave description of condensate micro-motion in a time-averaged orbiting potential
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Solitary-wave description of condensate micro-motion in a
time-averaged orbiting potential trap
K J Challis? and R J Ballagh
Department of Physics, University of Otago, PO Box 56, Dunedin, New Zealand
C W Gardiner
School of Chemical and Physical Sciences, Victoria University, Wellington, New Zealand
(Dated: February 2, 2008)
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 be-
haviour 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.
1. INTRODUCTION
The Time-averaged Orbiting Potential (TOP) trap [1]
was an important tool in the realization of Bose-Einstein
condensates, and it remains a common method for mag-
netically trapping atoms. Early theoretical descriptions
of the TOP trap used two approximations: the adiabatic
approximation, which assumes that the magnetic dipoles
of the atoms align instantaneously to the magnetic field,
and the time-average approximation, where the time dy-
namics of the trapping fields are neglected on the time
scale of the motion of the trapped atoms. Under these as-
sumptions, the TOP trap is represented by a static, har-
monic potential and the condensate eigenstates are rela-
tively easily calculated (usually by numerical means) and
are s
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