Ground-State Wave Function With Interactions Between Different Species In M-Component Miscible Bose-Einstein Condensates

We construct a variational ground-state wave function of weakly interacting M-component Bose Einstein condensates beyond the mean-field theory by incorporating the dynamical 3/2-body processes, where one of the two colliding particles drops into the condensate and vice versa. Our numerical results with various masses and particle numbers show that the 3/2-body processes between different particles make finite contributions to lowering the ground-state energy, implying that many-body correlation effects between different particles are essential even in the weak-coupling regime of the Bose - Einstein condensates. We also consider the stability condition for 2-component miscible states using the new ground-state wave function. Through this calculation, we obtain the relation U-AB(2)/UAAUBB < 1 + alpha, where U-ij is the effective contact potential between particles i and j and a is the correction, which originates from the 3/2- and 2-body processes.