Calculation of drag and superfluid velocity from the microscopic parameters and excitation energies of a two-component Bose-Einstein condensate in an optical lattice

We investigate a model of a two-component Bose-Einstein condensate residing in an optical lattice. Within a Bogoliubov approach at the mean-field level, we derive exact analytical expressions for the excitation spectrum of the two-component condensate when taking into account hopping and interactions between arbitrary sites. Our results thus constitute a basis for works that seek to clarify the effects of higher-order interactions in the system. We investigate the excitation spectrum and the two branches of superfluid velocity in more detail for two limiting cases of particular relevance. Moreover, we relate the hopping and interaction parameters in the effective Bose-Hubbard model to microscopic parameters in the system, such as the laser light wavelength and atomic masses of the components in the condensate. These results are then used to calculate analytically and numerically the drag coefficient between the components of the condensate. We find that the drag is most effective close to the symmetric case of equal masses between the components, regardless of the strength of the intercomponent interaction and the lattice well depth.

Figure 1

(Color online) An optical lattice setup by counterpropagating lasers serves as a potential landscape for two atomic species, denoted by the red (dark) and green (light) spheres. Each species of atoms may hop from site to site and also interact with both interspecies and intraspecies atoms.

Figure 2

(Color online) The physical scenario expressed by Eq. (23).

Figure 3

(Color online) Plot of the superfluid velocity for the two quasiparticle branches ${\mathit{v}}_{\pm }$. Above, we have used the dimensionless parameters ${\zeta }_{\alpha }=-t_{\alpha }{F}_{\alpha }{a}^2$ and $\rho ={\gamma }_{AB}^2/\left({\gamma }_A{\gamma }_B\right)$. The latter is a measure for the interaction between the two atomic components in the condensate.

Figure 4

(Color online) Plot of the hopping and interaction parameters in the Bose-Hubbard model as a function of the trap depth $s=V_0/E_R$.

Figure 5

(Color online) Contour plot of the normalized drag coefficient ${\rho }_d/{\rho }_0$ as a function of the mass ratio $m_A/m_B$ and the lattice well depth $s$. Two different values of $\eta$ have been used, corresponding to weak $\left(\eta =0.2\right)$ and strong $\left(\eta =0.8\right)$ intercomponent scattering.