Ground-State Wave Function with Interactions between Different Species in $M$-Component Miscible Bose-Einstein Condensates

TL;DR

This paper develops a variational ground-state wave function for multi-component Bose-Einstein condensates that includes complex many-body correlations, revealing their importance even in weakly interacting regimes.

Contribution

It introduces a novel variational wave function incorporating 3/2-body processes, extending beyond mean-field theory for multi-component BECs.

Findings

3/2-body processes significantly lower the ground-state energy

Many-body correlations are essential even in weak-coupling regimes

Derived a stability condition involving effective contact potentials

Abstract

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 $U^{2}_{AB}/U_{AA}U_{BB}<1+\alpha$, where $U_{ij}$ is the effective contact potential between particles $i$ and $j$ and $\alpha$ is the correction, which originates from the $3/2$-body and $2$-body processes.