Hyperspherical approach to dipolar Bose-Einstein condensates beyond the mean-field limit

TL;DR

This paper introduces a hyperspherical method to analyze dipolar Bose-Einstein condensates, incorporating beyond-mean-field effects to accurately describe self-bound droplets and their excitations.

Contribution

It establishes a general correspondence between hyperspherical methods and Gaussian ansatz, enabling the inclusion of beyond-mean-field effects in dipolar BECs.

Findings

Accurately describes energies and wavefunctions of dipolar droplets

Extends hyperspherical approach to include beyond-mean-field effects

Provides a unified framework for various interparticle potentials

Abstract

We apply a hyperspherical formulation to a trapped Bose-Einstein condensate with dipolar and contact interactions. Central to this approach is a general correspondence between K-harmonic hyperspherical methods and a suitable Gaussian ansatz to the Gross-Pitaevskii equation, regardless of the form of the interparticle potential. This correspondence allows one to obtain hyperspherical potential energies for a wide variety of physical problems. In the case of the dipolar Bose-Einstein condensate, this motivates the inclusion of a beyond-mean field term within the hyperspherical picture, which allows us to describe the energies and wavefunctions of excitations of self-bound dipolar droplets outside of the mean-field limit.