Master's Thesis: Excitation Spectrum of a Weakly Interacting Spin-Orbit Coupled Bose-Einstein Condensate

TL;DR

This thesis develops an analytic framework to study the excitation spectrum of a weakly interacting, spin-orbit coupled Bose-Einstein condensate in a lattice, revealing new phase behaviors and including previously neglected linear excitation effects.

Contribution

It introduces a novel analytical approach that incorporates linear excitation terms to analyze phase diagrams and excitation spectra of spin-orbit coupled Bose gases in optical lattices.

Findings

Identified five distinct phases with their excitation spectra and superfluid velocities.

Confirmed phase diagrams through free energy minimization including excitation effects.

Discovered bosonic analogues of Fulde-Ferrell-Larkin-Ovchinnikov states.

Abstract

A weakly interacting, spin-orbit coupled, two-component, ultracold Bose gas bound to a Bravais lattice is studied. Motivated by recent experimental advances in the field of synthetically spin-orbit coupled, ultracold, neutral atomic gases showing Bose-Einstein condensation, an analytic framework with which to describe such systems in the superfluid regime is presented. This is applied to a Rashba spin-orbit-coupled Bose gas in a two-dimensional optical lattice. The exotic nature of Bose-Einstein condensation in the presence of spin-orbit coupling is an interesting study by itself. Additionally, when the optical lattice is introduced, the system provides a highly controllable experimental testing ground for numerous condensed matter physics phenomena. Five phases of the system are considered, and their excitation spectra, critical superfluid velocities and free energies are found. In obtaining the free energy, the effects of terms in the Hamiltonian that are linear in excitation operators are included, and such terms have not been studied previously in this context. Minimization of the free energy at zero temperature is used to confirm the phase diagrams reported in the literature, where it has usually been obtained by neglecting the effect of excitations. The plane and stripe wave phases in the phase diagram are bosonic analogues of Fulde-Ferrell-Larkin-Ovchinnikov states in superconductors involving nonzero condensate momenta.