Bright-like soliton solution in quasi-one-dimensional BEC in third order on interaction radius

TL;DR

This paper derives an exact soliton solution in quasi-one-dimensional Bose-Einstein condensates considering third-order interaction effects, revealing new soliton behaviors beyond the Gross-Pitaevskii approximation.

Contribution

It introduces a third-order interaction radius approach in quantum hydrodynamics, providing analytical soliton solutions and conditions for their existence in BECs.

Findings

New soliton solutions in BECs with third-order interaction effects

Existence conditions depend on scattering length and particle concentration

Potential for more detailed interaction potential analysis

Abstract

Nonlinear Schr\"{o}dinger equations and corresponding quantum hydrodynamic (QHD) equations are widely used in studying ultracold boson-fermion mixtures and superconductors. In this article, we show that a more exact account of interaction in Bose-Einstein condensate (BEC), in comparison with the Gross-Pitaevskii (GP) approximation, leads to the existence of a new type of solitons. We use a set of QHD equations in the third order by the interaction radius (TOIR), which corresponds to the GP equation in a first order by the interaction radius. The solution for the soliton in a form of expression for the particle concentration is obtained analytically. The conditions of existence of the soliton are studied. It is shown what solution exists if the interaction between the particles is repulsive. Particle concentration of order of $10^{12}$-$10^{14}$ $cm^{-3}$ has been achieved experimentally for the BEC, the solution exists if the scattering length is of the order of 1 $\mu$m, which can be reached using the Feshbach resonance. It is one of the limit case of existence of new solution. The corresponding scattering length decrease with the increasing of concentration of particles. The investigation of effects in the TOIR approximation gives a more detail information on interaction potentials between the atoms and can be used for a more detail investigation into the potential structure.