Analytical solutions of the coupled Gross-Pitaevskii equations for the three-species Bose-Einstein condensates

TL;DR

This paper analytically solves the coupled Gross-Pitaevskii equations for three-species Bose-Einstein condensates, classifying spatial configurations and their parameter dependencies under the Thomas-Fermi approximation.

Contribution

It provides analytical solutions and a comprehensive classification of spatial configurations in three-species BECs, including zone boundaries and parameter sensitivity analysis.

Findings

Six types of spatial configurations identified.

Parameter-space divided into zones with specific configurations.

Regions with high sensitivity to parameters discovered.

Abstract

The coupled Gross-Pitaevskii equations for the g.s. of the three-species condensates (3-BEC) have been solved analytically under the Thomas-Fermi approximation. Six types of spatial configurations in miscible phase are found. The whole parameter-space has been divided into zones each supports a specific configuration (miscible or immiscible). The borders of the zones are described by analytical formulae. Due to the division, the variation of the spatial configuration against the parameters can be visualized, and the effects of the parameters can be thereby understood. There are regions in the parameter-space where the configuration is highly sensitive to the parameters. These regions are tunable and valuable for the determination of the parameters.