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.
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.
Motivated by previous work on drag effects in superfluid Bose-Einstein condensates, the Bose-Hubbard model on the square lattice is considered using mean-field theory, and a method for computing the superfluid drag density that does not rely on Galilean invariance is employed to re-derive the drag in the weakly interacting two-component Bose-Einstein condensate. The same method is then used on the Bose-Hubbard model generalized to three-components. An exact analytic expression is not possible because of the complexity of the resulting diagonalization problem. However, Rayleigh-Schrödinger perturbation theory is used to fourth order, which yields an analytic perturbative expression for the zero temperature drag, in addition to exact numerical diagonalization to find the exact behaviour at zero and finite temperatures within mean-field theory. It is found that the presence of a third component can alter the drag in a non-trivial manner: The drag between the two initial boson components can be completely mediated by the third, and it can be both enhanced and diminished depending on the inter-component interaction strengths and signs. An attempt is also made at finding the drag in a weakly interacting two-component Bose-Einstein condensate with spin-orbit coupling, but complications arise, which are discussed. Finally, a phase diagram for the two-component condensate with interactions and spin-orbit coupling is constructed, describing the spin-imbalance, degeneracy, and distribution of spin at zero temperature. A qualitative discussion of the finite temperature behaviour suggests that the inhomogeneous weakly interacting and spin-orbit coupled superfluid Bose-Einstein condensate may in some regions in parameter space favor spin-imbalance as the temperature is increased.
We investigate the spectrum of spin conductivity for a miscible two-component Bose-Einstein condensate (BEC) that exhibits spin superfluidity. By using the Bogoliubov theory, the regular part being the spin conductivity at finite ac frequency and the spin Drude weight characterizing the $\ensuremath{\delta}$-function peak at zero frequency are analytically computed. We demonstrate that the spectrum exhibits a power-law behavior at low frequency, reflecting gapless density and spin modes specific to the binary BEC. At the phase transition points into immiscible and quantum-droplet states, the change in quasiparticle dispersion relations modifies the power law. In addition, the spin Drude weight becomes finite, indicating zero spin resistivity due to spin superfluidity. Our results also suggest that the Andreev-Bashkin drag density is accessible by measuring the spin conductivity spectrum.
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 mean-field level, Rayleigh-Schr\"odinger 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 intercomponent 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 intercomponent interaction ${\ensuremath{\gamma}}_{AB}$ between the two components
A and
B. The increase is independent of the sign of the intercomponent 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 nonmonotonic function of the intercomponent interaction strength ${\ensuremath{\gamma}}_{AC}$ between
A and a third component
C. For weak ${\ensuremath{\gamma}}_{AC}$ compared to the direct interaction ${\ensuremath{\gamma}}_{AB}$ between
A and
B, the drag coefficient between
A and
B can decrease, contrary to what one naively would expect. When ${\ensuremath{\gamma}}_{AC}$ is strong compared to ${\ensuremath{\gamma}}_{AB}$, the drag between
A and
B increases with increasing ${\ensuremath{\gamma}}_{AC}$, as one would naively expect. We attribute the subtle reduction of ${\ensuremath{\rho}}_{d,AB}$ with increasing ${\ensuremath{\gamma}}_{AC}$, which has no counterpart in the two-component case, to a renormalization of the intercomponent scattering vertex ${\ensuremath{\gamma}}_{AB}$ via intermediate excited states of the third condensate
C. We briefly comment on how this generalizes to systems with more than three components.
A microscopic theory of a nondissipative drag in a two-component superfluid Bose gas is developed. The expression for the drag current in the system with the components of different atomic masses, densities, and scattering lengths is derived. It is shown that the drag current is proportional to the square root of the gas parameter. The temperature dependence of the drag current is studied and it is shown that at temperature of order or smaller than the interaction energy the temperature reduction of the drag current is rather small. A possible way of measuring the drag factor is proposed. A toroidal system with the drag component confined in two half-ring wells separated by two Josephson barriers is considered. Under certain condition such a system can be treated as a Bose-Einstein counterpart of the Josephson charge qubit in an external magnetic field. It is shown that the measurement of the difference of number of atoms in two wells under a controlled evolution of the state of the qubit allows one to determine the drag factor.