Beyond Fermi pseudopotential: a modified GP equation

TL;DR

This paper introduces a modified Gross-Pitaevskii equation incorporating energy-dependent interactions, improving the accuracy of ground state energy predictions for trapped condensates, especially under strong confinement or high density.

Contribution

It develops an effective potential and a modified GP equation that include shape-dependent confinement corrections based on the effective-range expansion.

Findings

Improved agreement with diffusion Monte Carlo calculations.

Shape dependence becomes significant in strong confinement or high-density regimes.

Provides a more accurate description of atom-atom interactions in quantum systems.

Abstract

We present an effective potential and the corresponding modified Gross-Pitaevskii equation that account for the energy dependence of the two-body scattering amplitude through an effective-range expansion. For the ground state energy of a trapped condensate, the theory leads to what we call a shape-dependent confinement correction that improves agreements with diffusion Monte Carlo calculations. The theory illustrates, for relatively strong confinement and/or high density, how the shape dependence on atom-atom interaction can come into play in a many-atom quantum system.