Interaction of two alkali atom Bose-Einstein condensates in a harmonic trapping potential

Abstract

We analyze, using the Gross-Pitaevskii equation, the interaction between two alkali atom Bose-Einstein condensates (BECs) that are trapped in an isotropic harmonic potential. Assuming that both BECs can initially be described in terms of Gaussian wave functions prior to interaction, we show that the resulting energy functional of the two interacting condensates has a unique minimum value, subject to certain conditions obeyed by the spatial separation between the maxima of both condensate wavefunctions as well as their respective variances. The results presented in this work imply that it is possible to prepare minimum position uncertainty many-body quantum states by having two trapped BECs interact with each other in such a way that the total energy of both BECs is minimized, and at the same time presents a computationally simple yet physically insightful approach to analyzing the dynamics of interacting many-body ultracold atom gases.