Calculation of Drag and Superfluid Velocity from the Microscopic Parameters and Excitation Energies of a Two-Component Bose-Einstein Condensate on an Optical Lattice

We investigate a model of a two-component Bose-Einstein condensate residing on an optical lattice. Within a Bogolioubov-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 laserlight 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.

💡 Research Summary

The paper presents a comprehensive theoretical study of a two‑component Bose‑Einstein condensate (BEC) confined in an optical lattice, focusing on the calculation of the drag (mutual friction) and the superfluid velocities of each component from microscopic system parameters. Starting from a generalized Bose‑Hubbard Hamiltonian that includes hopping amplitudes (t_{ij}^{\alpha}) and interaction matrix elements (U_{ij}^{\alpha\beta}) for arbitrary lattice sites (not limited to nearest‑neighbour terms), the authors apply a mean‑field Bogoliubov approach. By introducing condensate order parameters (\psi_{\alpha}=\langle a_{i\alpha}\rangle) for the two species (\alpha=A,B) and performing a Bogoliubov transformation, they derive an exact 4×4 eigenvalue problem whose solutions give two gapless Goldstone modes and one gapped mixed mode. The resulting excitation spectra can be written compactly as

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