An effective potential for one-dimensional matter-wave solitons in an axially inhomogeneous trap

Details An effective potential for one-dimensional matter-wave solitons in an axially inhomogeneous trap An effective potential for one-dimensional matter-wave solitons in an axially inhomogeneous trap

2006-07-27

arxiv.org/abs/cond-mat/0607726v1

Physics

Condensed Matter

Soft Condensed Matter

to be published in Physics Letters A

Scientific paper

10.1016/j.physleta.2006.07.062

We demonstrate that a tight transverse trap with the local frequency, $% \omega_{\perp}$, gradually varying in the longitudinal direction ($x$) induces an effective potential for one-dimensional solitons in a self-attractive Bose-Einstein condensate. An analytical approximation for this potential is derived by means of a variational method. In the lowest approximation, the potential is $N(S+1)\omega_{\perp}(x)$, with $N$ the soliton's norm (number of atoms), and $S$ its intrinsic vorticity (if any). The results can be used to devise nonuniform traps helping to control the longitudinal dynamics of the solitons. Numerical verification of the analytical predictions will be presented elsewhere.

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