Superfluid drag of two-species Bose-Einstein condensates in optical lattices

We study two-species Bose-Einstein condensates in quasi-two-dimensional optical lattices of varying geometry and potential depth. Based on the numerically exact Bloch and Wannier functions obtained using the plane-wave expansion method, we quantify the drag (entrainment coupling) between the condensate components. This drag originates from the (short-range) interspecies interaction and increases with the kinetic energy. As a result of the interplay between interaction and kinetic energy effects, the superfluid-drag coefficient shows a nonmonotonic dependence on the lattice depth. To make contact with future experiments, we quantitatively investigate the drag for mass ratios corresponding to relevant atomic species.

Figure 1

Optical-lattice potentials in units of the recoil energy $E_R=k^2/2m_A$ with their minima set equal to zero. (a) 3BTL, (b) 3BSL, and (c) 4BSL. For these plots $V_0=-E_R/2$.

Figure 2

Superfluid drag for different lattices and interaction strengths: (a) and (b) three-beam triangular lattice (3BTL), (c) and (d) three-beam square lattice (3BSL), and (e) and (f) four-beam square lattice (4BSL). The left column [(a), (c), (e)] corresponds to weak interspecies interactions $a_{AB}=30a_0$ and the right column [(b), (d), (f)] corresponds to strong ones, $a_{AB}=64a_0$. Note the different scales for the color scheme.

Figure 3

Superfluid drag in a 3BTL as a function of the lattice depth $V_0$ for fixed mass ratios corresponding to the mixtures ${}^{87}$Rb-${}^{85}$Rb ($m_B/m_A\approx 1$, solid), ${}^{87}$Rb-${}^{41}$K ($m_B/m_A\approx 2.2$, dashed), and ${}^{87}$Rb-${}^{23}$Na ($m_B/m_A\approx 3.8$, dotted). Component $B$ corresponds to ${}^{87}$Rb in all three cases. The interspecies scattering length is set to $a_{AB}=64a_0$.

Figure 4

Superfluid drag in a 3BTL (not normalized with $n_A$) as a function of the particle densities for $A={}^{85}$Rb and a lattice depth $V_0=-1.2E_R$, which maximizes the drag for this mass ratio (see Fig. 3). The other parameter values are the same as in Fig. 2b. Component $B$ corresponds to the more weakly interacting species.