Thomas-Fermi Approximation for a Condensate with Higher-order Interactions

TL;DR

This paper extends the Thomas-Fermi approximation to Bose-Einstein condensates by including effective-range corrections, providing analytical solutions for the ground state and discussing experimental tunability.

Contribution

It introduces an analytical approach to include effective-range corrections in the Thomas-Fermi approximation for condensates, enhancing the understanding of higher-order interaction effects.

Findings

Analytical solutions for chemical potential and condensate profiles with effective-range corrections.

Comparison showing differences from the standard Thomas-Fermi approach.

Discussion on experimental tunability of effective-range effects.

Abstract

We consider the ground state of a harmonically trapped Bose-Einstein condensate within the Gross-Pitaevskii theory including the effective-range corrections for a two-body zero-range potential. The resulting non-linear Schr\"odinger equation is solved analytically in the Thomas-Fermi approximation neglecting the kinetic energy term. We present results for the chemical potential and the condensate profiles, discuss boundary conditions, and compare to the usual Thomas-Fermi approach. We discuss several ways to increase the influence of effective-range corrections in experiment with magnetically tunable interactions. The level of tuning required could be inside experimental reach in the near future.