Energy dependent scattering and the Gross-Pitaevskii Equation in two dimensional Bose-Einstein condensates

TL;DR

This paper investigates how energy-dependent scattering affects the Gross-Pitaevskii equation in 2D Bose-Einstein condensates, revealing significant differences from 3D cases and providing numerical solutions for hard-sphere bosons.

Contribution

It introduces a self-consistent approach using the off-shell two-body T-matrix to derive effective interactions and Gross-Pitaevskii equations in 2D Bose gases, highlighting dimensional effects.

Findings

Interaction strength is greater in 2D than in 3D for the same particle size.

The Thomas-Fermi regime is reached at lower populations in 2D.

Vortex creation energy is reduced in 2D condensates.

Abstract

We consider many-body effects on particle scattering in one, two and three dimensional Bose gases. We show that at zero temperature these effects can be modelled by the simpler two-body T-matrix evaluated off the energy shell. This is important in 1D and 2D because the two-body T-matrix vanishes at zero energy and so mean-field effects on particle energies must be taken into account to obtain a self-consistent treatment of low energy collisions. Using the off-shell two-body T-matrix we obtain the energy and density dependence of the effective interaction in 1D and 2D and the appropriate Gross-Pitaevskii equations for these dimensions. We present numerical solutions of the Gross-Pitaevskii equation for a 2D condensate of hard-sphere bosons in a trap. We find that the interaction strength is much greater in 2D than for a 3D gas with the same hard-sphere radius. The Thomas-Fermi regime is therefore approached at lower condensate populations and the energy required to create vortices is lowered compared to the 3D case.