Dilute Bose gases interacting via power-law potentials

TL;DR

This paper investigates how dilute Bose gases with power-law interactions, specifically van der Waals and longer-range r^{-4} potentials, are affected by interaction corrections beyond the scattering length approximation, using analytical and numerical methods.

Contribution

It introduces a parameterization of interaction corrections in dilute Bose gases with power-law potentials, extending analysis from van der Waals to longer-range interactions.

Findings

Quantified energy corrections for two- and few-atom systems

Generalized results to r^{-4} interaction potentials

Provided analytical and numerical solutions for confined systems

Abstract

Neutral atoms interact through a van der Waals potential which asymptotically falls off as r^{-6}. In ultracold gases, this interaction can be described to a good approximation by the atom-atom scattering length. However, corrections arise that depend on the characteristic length of the van der Waals potential. We parameterize these corrections by analyzing the energies of two- and few-atom systems under external harmonic confinement, obtained by numerically and analytically solving the Schrodinger equation. We generalize our results to particles interacting through a longer-ranged potential which asymptotically falls off as r^{-4}.