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

Abstract

We demonstrate that a tight transverse trap with the local frequency, , 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.

to be published in Physics Letters A

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• Matter-wave vortices in cigar-shaped and toroidal waveguides
• Gap solitons in a model of a superfluid fermion gas in optical lattices
• Bose-Einstein condensates under a spatially-modulated transverse confinement
• Gap solitons in superfluid boson-fermion mixtures
• Collapse instability of solitons in the nonpolynomial Schrödinger equation with dipole-dipole interactions
• Stable dipole solitons and soliton complexes in the nonlinear Schrodinger equation with periodically modulated nonlinearity
• Quasi-one-dimensional approximation for Bose-Einstein condensates transversely trapped by a funnel potential
• Controlled self-similar matter waves in PT-symmetric waveguide
• Acoustic analogue of Hawking radiation in quantized circular superflows of Bose-Einstein condensates
• Stability and collapse of localized solutions of the controlled three-dimensional Gross-Pitaevskii equation
• Dynamics of kicked matter-wave solitons in an optical lattice