Hydrodynamic model of BEC with anisotropic short range interaction and the bright solitons in the repulsive BEC

TL;DR

This paper develops a quantum hydrodynamic model for anisotropic short-range interactions in Bose-Einstein condensates (BECs), analyzing stability and bright soliton formation in repulsive BECs with nonlocal effects.

Contribution

It introduces a third-order interaction model with multiple interaction constants, extending the Gross-Pitaevskii approximation to include anisotropic effects and nonlocal nonlinearities.

Findings

Identifies conditions for stability and instability in anisotropic BECs.

Shows existence of bright solitons in repulsive BECs under anisotropic interactions.

Demonstrates reduction of nonlocal effects to quintic nonlinearity for soliton description.

Abstract

The quantum hydrodynamic model is developed for the axial symmetric anisotropic short-range interaction. The quantum stress tensor presents the interaction. It is derived up to the third order by the interaction radius. The first order by the interaction radius contains the isotropic part only. It leads to the interaction in the Gross-Pitaevskii approximation. Terms existing in the third order by the interaction radius are caused by the isotropic and nonisotropic parts of the interaction. Each of them introduces the interaction constant. Therefore, three interaction constants are involved in the model. Atoms, except the alkali and alkali-earth atoms, can have anisotropic potential of interaction, particularly it is demonstrated for the lanthanides. The short-wavelength instability caused by the nonlocal terms appears in the Bogoliubov spectrum. Conditions for the stable and unstable behaviour are described. Bright solitons in the repulsive BEC are studied under influence of the anisotropic short-range interaction in the BEC of one species. Area of existence of this bright solitons corresponds to the area of the instability of the Bogoliubov spectrum. Approximate reduction of the nonlocal nonlinearity to the quintic nonlinearity at the description of the bright solitons is demonstrated either.