Analytic Study of Ultracold, Synthetically Spin–Orbit Coupled, Weakly Interacting, Two-Component Bose Gases Residing on Bravais Lattices

Abstract

In this Master's thesis, the behavior of ultracold, synthetically spin orbit coupled, weakly interacting, two-component Bose gases residing on Bravais lattices, is explored analytically. In particular, utilizing a mean field approach, general expressions for the chemical potentials are deduced for the superfluid phase, and non-diagonal expressions for the Hamiltonian are subsequently provided. An application of these expressions is presented for the case of a pure condensate residing on a square lattice, yielding an analytically derived phase diagram that coincides with numerical results found in the literature. Finally, future continuations of this work are suggested.