Superfluid Drag in Multicomponent Bose-Einstein Condensates on a Square Optical Lattice

The superfluid drag-coefficient of a weakly interacting three-component Bose-Einstein condensate is computed deep into the superfluid phase, starting from a Bose-Hubbard model with component-conserving, on-site interactions and nearest-neighbor hopping. Rayleigh-Schr\"odinger perturbation theory is employed to provide an analytic expression for the drag density. In addition, the Hamiltonian is diagonalized numerically to compute the drag within mean-field theory at both zero and finite temperatures to all orders in inter-component interactions. Moreover, path integral Monte Carlo simulations have been performed to support the mean-field results. In the two-component case the drag increases monotonically with the magnitude of the inter-component interaction $\gamma_{AB}$ between the two components A and B. This no longer holds when an additional third component C is included. Instead of increasing monotonically, the drag can either be strengthened or weakened depending on the details of the interaction strengths, for weak and moderately strong interactions. The general picture is that the drag-coefficient between component A and B is a non-monotonic function of the inter-component interaction strength $\gamma_{AC}$ between A and a third component C. For weak $\gamma_{AC}$ compared to the direct interaction $\gamma_{AB}$ between A and B, the drag-coefficient between A and B can {\it decrease}, contrary to what one naively would expect. When $\gamma_{AC}$ is strong compared to $\gamma_{AB}$, the drag between A and B increases with increasing $\gamma_{AC}$, as one would naively expect. We attribute the subtle reduction of $\rho_{d,AB}$ with increasing $\gamma_{AC}$, which has no counterpart in the two-component case, to a renormalization of the inter-component scattering vertex $\gamma_{AB}$ via intermediate excited states of the third condensate $C$.