Hyperspherical-LOCV Approximation to Resonant BEC

TL;DR

This paper introduces a hyperspherical LOCV approach to analyze the ground state of trapped bosons with varying scattering lengths, providing semi-quantitative energies and contact estimates even at unitarity.

Contribution

It develops a hyperspherical coordinate-based LOCV method to study strongly interacting Bose gases, including at infinite scattering length, offering analytical estimates for large N.

Findings

Provides energy per particle scaling as 2.5 N^{1/3} ħω.

Estimates two-body contact as 16 N^{1/6} sqrt(mω/ħ).

Achieves semi-quantitative results at unitarity.

Abstract

We study the ground state properties of a system of $N$ harmonically trapped bosons of mass $m$ interacting with two-body contact interactions, from small to large scattering lengths. This is accomplished in a hyperspherical coordinate system that is flexible enough to describe both the overall scale of the gas and two-body correlations. By adapting the lowest-order constrained variational (LOCV) method, we are able to semi-quantitatively attain Bose-Einstein condensate ground state energies even for gases with infinite scattering length. In the large particle number limit, our method provides analytical estimates for the energy per particle $E_0/N \approx 2.5 N^{1/3} \hbar \omega$ and two-body contact $C_2/N \approx 16 N^{1/6}\sqrt{m\omega/\hbar}$ for a Bose gas on resonance, where $\omega$ is the trap frequency.