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

TL;DR

This paper derives an effective potential for one-dimensional matter-wave solitons in a Bose-Einstein condensate with a longitudinally varying transverse trap, enabling better control of soliton dynamics.

Contribution

It introduces an analytical approximation for the effective potential induced by a varying transverse trap in a BEC, aiding in soliton control strategies.

Findings

Derived an analytical form of the effective potential for solitons

Showed the potential depends on soliton norm and vorticity

Provided a basis for designing nonuniform traps for soliton management

Abstract

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.