Beyond Thomas--Fermi analysis of the density profiles of a miscible two-component Bose--Einstein condensate

TL;DR

This paper extends Thomas--Fermi analysis to derive universal density boundary equations for a two-component Bose--Einstein condensate, providing analytical and numerical tools for understanding phase boundaries in various dimensions.

Contribution

It introduces a universal equation for density boundaries and a simplified procedure for solving the Thomas--Fermi approximation in 1D, 2D, and 3D.

Findings

Derived universal boundary equations in all dimensions

Reduced complexity of Thomas--Fermi problem for separated phases

Analytically determined the phase boundary between regimes

Abstract

We investigate a harmonically trapped two-component Bose--Einstein condensate within the miscible regime, close to its boundaries, for different ratios of effective intra- and inter-species interactions. We derive analytically a universal equation for the density around the different boundaries in one, two and three dimensions, for both the coexisting and spatially separated regimes. We also present a general procedure to solve the Thomas--Fermi approximation in all three spatial dimensionalities, reducing the complexity of the Thomas--Fermi problem for the spatially separated case in one and three dimensions to a single numerical inversion. Finally, we analytically determine the frontier between the two different regimes of the system.