|dc.description.abstract||Spin-1 Bose-Einstein condensates present a wealth of physics, owing to the spin and superfluid order they possess. In this work, we consider spin-1 condensates with antiferromagnetic interactions, which favor the formation of spin-nematic order. Such condensates may exist in an easy-plane polar phase, and can support various topological defects with associated mass and spin currents. One defect of particular importance is the half-quantum vortex, which possesses both mass and spin circulation. The half-quantum vortex is equivalently realized in binary and easy-plane polar spin-1 condensates, and has been well-characterized theoretically, and observed in experiments. Another defect of interest is the nematic spin vortex, which possesses spin circulation, yet no mass circulation. The nematic spin vortex is thought to be unstable against decay into a pair of half quantum vortices. However, prior to this work, there was no general theory of nematic spin vortex stability.
In this thesis, we develop formalism describing the structure and excitation spectra of axis-symmetric vortices in easy-plane polar spin-1 condensates. We apply this formalism to systematically investigate the structure and linear stability of nematic spin vortices in a uniform system, finding a parameter regime where they may exist as stable defects. We verify our stability predictions with dynamical simulations.
Accurate numerical treatment of the stationary states and excitations of the nematic spin vortex in a uniform system has proved challenging due to the interplay of unstable and Nambu-Goldstone modes. Indeed, we found standard approaches to be ineffective. In this research we have developed new numerical schemes to resolve this issue, ultimately arriving at a robust approach able to provide sufficiently accurate results to illustrate the physics of the system.
Investigation of our results should be possible in current experiments with sodium spin-1 condensates. Here the nematic spin vortices we describe could have implications for the non-equilibrium dynamics following phase transitions between magnetic phases. Furthermore, the numerical and analytic methods we have developed here will have immediate applications to other types of vortices in spin-1 condensates.||