Two-species Bose-Einstein condensate in an optical lattice: analytical approximate formul\ae

TL;DR

This paper develops explicit analytical solutions for two-species Bose-Einstein condensates in optical lattices using variational and perturbation methods, aiding understanding of their density profiles and miscibility.

Contribution

It introduces a novel analytical approach to approximate solutions of coupled GPEs for two-species BECs in optical lattices, complementing numerical methods.

Findings

Explicit formulas for chemical potentials and wavefunctions derived.

Quantitative comparison with numerical solutions validates the analytical approach.

Highlights the importance of explicit solutions for characterizing density profiles and miscibility.

Abstract

Employing a general variational method and perturbation theory, we derived explicit solutions for the description of one-dimensional two species Bose-Einstein condensates confined by a harmonic trap potential in an optical lattice. We consider the system of two coupled Gross-Pitaevkii equations (GPE) and derive explicit expressions for the chemical potentials and wavefunctions in terms of the atom-atom interaction parameters and laser intensity. We have compared our results with the numerical solutions of the GPE and performed a quantitative analysis for the both considered methods. We underline the importance of the obtained explicit solutions to characterize the density profile or degree of miscibility of the two components.