Trapped Bose gases with large positive scattering length

TL;DR

This paper investigates the properties of trapped Bose gases with large positive scattering lengths, revealing that the system's energy and condensate fraction become independent of the scattering length and converge to finite values.

Contribution

It demonstrates that for large positive scattering lengths, the system's energy and condensate fraction reach finite limits, differing from behaviors at smaller scattering lengths.

Findings

Energy and condensate fraction become independent of scattering length at large values.

Attractive potentials with a bound state behave differently from repulsive or zero-range models.

System properties converge to finite constants when scattering length is large.

Abstract

We calculate the energy and the condensate fraction of a system of trapped bosons interacting via a short-range two-body potential with positive scattering length. The potential is attractive and has a two-body bound state. When the scattering length is small compared to the trap length the system is model independent: all potential models -- attractive, repulsive and zero-range -- provide similar results. When the scattering length is large the attractive model differs qualitatively from the repulsive and zero-range models. In this regime the system with attractive potential becomes independent of the scattering length, with both the energy and the condensate fraction converging towards finite constants.