Evaluation of Particle Numbers via Two Root Mean Square Radii in a 2-Species Bose–Einstein Condensate**Supported by the National Natural Science Foundation of China under Grant Nos. 11372122, 11274393, 11574404, and 11275279; the Open Project Program of State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, China; and the National Basic Research Program of China (2013CB933601); and Guangdong Natural Science Foundation (2016A030313313)

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 NA and NB 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 NA and NB.