Self-consistent Description of Bose-Bose Droplets: Harmonically Trapped Quasi-2D Droplets

TL;DR

This paper develops a self-consistent method to describe Bose-Bose quantum droplets confined by harmonic forces, accurately capturing their profiles and calculating the Lee-Huang-Yang correction both numerically and analytically in different regimes.

Contribution

It introduces a novel self-consistent approach to model quasi-2D Bose-Bose droplets, including an analytic form for the Lee-Huang-Yang potential in limiting cases.

Findings

Numerical method for beyond-mean-field chemical potential calculation.

Analytic expressions for Lee-Huang-Yang potential in strong and weak confinement limits.

Enhanced understanding of droplet profiles under harmonic confinement.

Abstract

We describe a quantum droplet of a Bose-Bose mixture squeezed by an external harmonic forces in one spatial direction. Our approach is based on the self-consistent method formulated in [1]. The true spatial droplet profile in the direction of confinement is accounted for, however local density approximation is assumed in the free directions. We define a numerical approach to find the beyond-mean-field contribution to the chemical potential (Lee-Huang-Yang chemical potential) -- the quantity that determines the droplet's profile. In addition to the numerical approach, we find the Lee-Huang-Yang potential in the analytic form in two limiting cases: a perturbative result for a strong confinement and a semiclassical expression when confinement is very weak.