Determining the interspecies interaction strength of a two-species Bose-Einstein condensate from the density profile of one species

TL;DR

This paper presents an analytical method to determine the interspecies interaction strength in a two-species Bose-Einstein condensate using only the density profile of one species, validated by numerical simulations.

Contribution

It introduces a simple analytical formula derived under the Thomas-Fermi approximation to measure interspecies interaction strength from single-species density data.

Findings

Analytical formula accurately estimates interspecies interaction strength.

Numerical simulations confirm the formula's validity for large condensates.

Provides a new experimental scheme complementing collisional measurement methods.

Abstract

We study harmonically trapped two-species Bose-Einstein condensates within the Gross-Pitaevskii formalism. By invoking the Thomas-Fermi approximation, we derive an analytical solution for the miscible ground state in a particular region of the system's parameter space. This solution furnishes a simple formula for determining the relative strength of the interspecies interaction from a measurement of the density distribution of only one of the two species. Accompanying numerical simulations confirm its accuracy for sufficiently large numbers of condensed particles. The introduced formula provides a condensate-based scheme that complements the typical experimental methods of evaluating interspecies scattering lengths from collisional measurements on thermal samples.