Superfluid drag in multicomponent Bose-Einstein condensates on a square optical lattice

Abstract

The superfluid drag-coefficient of a weakly interacting three-component Bose-Einstein condensate is computed on a square optical lattice deep in the superfluid phase, starting from a Bose-Hubbard model with component-conserving, on-site interactions and nearest-neighbor hopping. At the meanfield level, Rayleigh-Schrödinger 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, providing results beyond mean-field theory, 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 γAB between the two components A and B. The increase is independent of the sign of the inter-component interaction. 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 intercomponent interaction strength γAC between A and a third component C. For weak γAC compared to the direct interaction γAB between A and B, the drag-coefficient between A and B can decrease, contrary to what one naively would expect. When γAC is strong compared to γAB, the drag between A and B increases with increasing γAC , as one would naively expect. We attribute the subtle reduction of ρ d,AB with increasing γAC , which has no counterpart in the two-component case, to a renormalization of the inter-component scattering vertex γAB via intermediate excited states of the third condensate C. We briefly comment on how this generalizes to systems with more than three components.

Pairing and pair superfluid density in one-dimensional Hubbard models

“…This, of course, is expected from the relation between fermions and HCB via the JW transformation but it emphasizes the importance of finite size effects for small |U |. Another important feature is the lack of symmetry between U < 0 and U > 0, a feature which persists for soft core bosons contrary to mean field results [9][10][11].…”

“…However, when the coupling is strongly repulsive and the lattice filling is commensurate, supercounterflow can be observed [5][6][7][8]. The two-component DSF density was also studied with mean field [9][10][11] and quantum Monte Carlo (QMC) as was the three component case [11]. Mean field gives a DSF density proportional to the square of the interspecies interaction for the two-component case leading to the conclusion that this effect is independent of the sign of the coupling.…”

“…While there is obvious consensus that when the attraction is strong enough, the bosons are tightly paired and transport is only via pair superfluidity (PSF), there is no consensus on the weakly attractive case. Mean field calculations [9][10][11] show that for weak inter-species coupling, the DSF in the repulsive case is equivalent to the PSF in the attractive case and that the corresponding SF densities are symmetric with respect to the interaction sign. For bosons with strong, but finite, intra-species repulsion in one dimension, renormalization group calculations [16] argue that, for weak interaction, one needs a minimum attraction to form PSF and that PSF may co-exist with charge density wave (CDW).…”

Dissipationless Vector Drag--Superfluid Spin Hall Effect

“…The problem is amenable to analytical treatment only in the weakly interacting regime. Here, like in the case of the Andreev-Bashkin effect [23][24][25][26][27], the drag effects are expected to be inherently small. We will first demonstrate the existence of vector drag in the weakly interacting regime analytically.…”

“…The standard Andreev-Bashkin effect can be analytically calculated in macroscopic weakly interacting systems. That was previously done for square and triangular lattices, and in a continuum [23][24][25][26]. We begin by employing a similar analytic approach to establish the new phenomenon: the vector drag.…”