Dipolar Bose-Einstein Condensate with a Vortex
We theoretically consider the properties of a dipolar Bose-Einstein condensate with a vortex. Our theory includes the influence of the leading order quantum fluctuation corrections which allows the condensate to stabilize into a droplet state in the regime of dominant dipole interactions. We develop numerical techniques to accurately and efficiently calculate the stationary vortex states and the quasi-particle excitations. These methods are carefully benchmarked where possible. We make a brief study of self-bound vortex droplets, considering their basic properties, and presenting a phase diagram for where they exist. We also compare our calculations to results which appeared from another group during our research. We show that their results suffer from serious numerical issues and are unreliable. We focus on studying the properties of a vortex line in an elongated dipolar Bose-Einstein condensate confined by a prolate trap. Increasing the strength of the dipole-dipole interactions relative to the short ranged contact interactions we find that the system crosses over to a self-bound vortex droplet stabilized from collapse by quantum fluctuations. We calculate the quasiparticle excitation spectrum of the vortex state, which is important in characterizing the vortex response, and assessing its stability. When the DDIs are sufficiently strong we find that the vortex is dynamically unstable to quadrupolar modes.
Advisor: Blakie, Blair
Degree Name: Master of Science
Degree Discipline: Physics
Publisher: University of Otago
Keywords: Bose-einstein condensates; BEC; nonlinear; condensate; Gross-Pitaevskii; nonlinear Schrödinger equation; vortices; Collective excitations; vortex self-bound droplets; dipolar BEC; dipolar quantum; quantum fluctuations; Bogoliubov-de Gennes; instability; quadrupolar modes; dynamical stability; dipole interaction; density approximation; dipolar Bose-Einstein condensate; quasi-particle excitations; vortex; Hankel Transformation; Bessel function; cosine transformation; Cylindrical; BdG; Bogoliubov-de Gennes Equation; numerical calculations; DDI; dipole-dipole interactions; phonon dispersion; dynamical instability; eigenvalue problem; eigenvector; imaginary time evolution; laplacian operator; GPE; Gross–Pitaevskii equation; zero-norm; Kohn modes; Bessel grid; DDIs; numerical techniques; dipolar; dipolar BECs; LHY term; local density treatment; vortex stationary states; Kelvin wave (helical) excitations; stabilized from collapse; quasi-particle; leading order quantum fluctuation correction; lanthanides dysprosium; dysprosium; Dy; s-wave interaction; many-body physics
Research Type: Thesis