## Drag and Phases in Interacting and Spin-Orbit Coupled Superfluid Bose-Einstein Condensates

##### Master thesis

##### Permanent lenke

http://hdl.handle.net/11250/2501064##### Utgivelsesdato

2018##### Metadata

Vis full innførsel##### Samlinger

- Institutt for fysikk [2650]

##### Sammendrag

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.