Evaluation of the particle numbers via the two root mean square radii in a 2-species Bose-Einstein condensate

TL;DR

This paper derives analytical formulas relating particle numbers to root mean square radii in a two-species Bose-Einstein condensate using the Thomas-Fermi approximation, facilitating particle number evaluation.

Contribution

The paper introduces new analytical formulae linking particle numbers with root mean square radii in two-species BECs under TFA, specifically for centrally overlapping distributions.

Findings

Formulas accurately relate particle numbers to radii in the specified case.

TFA provides reliable results for the considered distribution.

Formulas are useful for experimental evaluation of particle numbers.

Abstract

The coupled Gross-Pitaevskii equations for two-species BEC have been solved analytically under the Thomas-Fermi approximation (TFA). Based on the analytical solution, two formulae are derived to relate the particle numbers $N_A$ and $N_B$ with the root mean square radii of the two kinds of atoms. Only the case that both kinds of atoms have nonzero distribution at the center of an isotropic trap is considered. In this case the TFA has been found to work nicely. Thus, the two formulae are applicable and are useful for the evaluation of $N_A$ and $N_B$.