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

TL;DR

This paper derives analytical expressions for the excitation spectrum and superfluid velocities of a two-component Bose-Einstein condensate on an optical lattice, relating microscopic parameters to macroscopic properties and calculating the intercomponent drag.

Contribution

It provides exact analytical formulas for excitation spectra and superfluid velocities, linking microscopic parameters to effective model parameters, and analyzes the intercomponent drag in the system.

Findings

Drag is most effective near equal mass components.

Derived explicit relations between microscopic and effective parameters.

Provided analytical and numerical calculations of the drag coefficient.

Abstract

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.