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

摘要

The coupled Gross-Pitaevskii equations for the ground state of the three-species condensates have been solved analytically under the Thomas-Fermi approximation. Six types of spatial configurations in the miscible phase are found. The whole parameter space has been divided into zones, each of which supports a specific configuration (miscible or immiscible). The boundaries 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 thereby be 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.