Ground-state solution of quantum droplets in Bose-Bose mixtures

TL;DR

This study develops an efficient numerical method to compute the ground states of quantum droplets in Bose-Bose mixtures, validating models and analyzing critical particle numbers with high accuracy.

Contribution

The paper introduces a robust gradient flow scheme for ground state computation and validates the density-locked model against full two-component systems.

Findings

Validated the density-locked model as a reliable approximation.

Established convergence rates of the Thomas-Fermi approximation in strong-coupling regimes.

Numerically determined the critical particle number for self-binding, refining previous analytical predictions.

Abstract

In this paper, we present a systematic study on the ground state computation of quantum droplets in homonuclear Bose-Bose mixtures, governed by the extended Gross-Pitaevskii equations (eGPEs) with Lee-Huang-Yang (LHY) corrections. This model captures the formation of self-bound droplets stabilized by the delicate balance between the attractive mean-field interaction and the repulsive quantum fluctuations. We formulate dimensionless energy functionals for both the general two-component system and the reduced single-component density-locked model. To compute the ground states efficiently, we adapt and benchmark various gradient flow discretization schemes, identifying a backward-forward sine-pseudospectral scheme based on the gradient flow with Lagrange multiplier method (GFLM-BFSP) as the robust solver for our simulations. Utilizing this method, we report three main numerical observations: (i) the density-locked model is quantitatively validated as a reliable approximation for ground state properties; (ii) the dimension-dependent convergence rates of the Thomas-Fermi approximation are established in the strong-coupling regime; and (iii) the critical particle number for self-binding in free space is numerically determined, providing a precise correction to the analytical prediction by Petrov [Phys. Rev. Lett. 115, 155302 (2015)].