Soliton localization in Bose-Einstein condensates with time-dependent harmonic potential and scattering length

TL;DR

This paper derives exact solitonic solutions for Bose-Einstein condensates under time-dependent harmonic traps and interactions, demonstrating indefinite localization of solitons under specific oscillating conditions, with potential experimental realization.

Contribution

It provides new exact solutions for the Gross-Pitaevskii equation with time-dependent parameters, revealing conditions for indefinite soliton localization.

Findings

Exact single- and multi-soliton solutions derived.

Solitons can be localized indefinitely with oscillating traps.

Experimental feasibility demonstrated for long-term localization.

Abstract

We derive exact solitonic solutions of a class of Gross-Pitaevskii equations with time-dependent harmonic trapping potential and interatomic interaction. We find families of exact single-solitonic, multi-solitonic, and solitary wave solutions. We show that, with the special case of an oscillating trapping potential and interatomic interaction, a soliton can be localized indefinitely at an arbitrary position. The localization is shown to be experimentally possible for sufficiently long time even with only an oscillating trapping potential and a constant interatomic interaction.