Vortex nucleation in a superfluid

Superfluids have very peculiar rotational properties as the Hess-Fairbank experiment spectacularly demonstrates. In this experiment, a rotating vessel filled with helium is cooled down past the critical temperature. Remarkably, as the liquid becomes superfluid, it gradually stops its rotation. This expulsion of vorticity, analogous to the Meissner effect, provides a fundamental experimental definition of superfluidity. As a consequence, superfluids not only posses quasiparticles like phonons, but also quantized vortex excitations. This thesis examines the creation mechanism of vortices, or nucleation, in the low temperature limit. At these temperatures, thermal activation of vortices is ruled out and nucleation must be a tunneling effect. Unfortunately, there is no theory to describe this nucleation process. Vortex nucleation is believed to more likely occur in the vicinity of irregularities of the vessel. We therefore consider a few simple, yet experimentally realistic, two-dimensional configurations to calculate nucleation rates. Close to zero temperature and within a certain approximation, the superfluid is inviscid and incompressible such that it can naturally be treated as an ideal two-dimensional fluid flow. Calculating the energy of static vortex configurations can then be done with standard hydrodynamics. The kinetic energy of the flow as a function of the position of the vortex then describes a potential barrier for vortex nucleation. Under rotation, the vortex-free state becomes metastable and can decay to a state with one or more vortices. In this thesis, we carry out a semiclassical calculation of the nucleation rate exponent. We use the WKB method along the path of least action created by the presence of a bump or wedge. This work is but a first approximation as fluctuations around this path can be added as well. The main purpose has been to lay down the groundwork required to include the dissipative effect of the coupling to phonons, which is paramount to an accurate description of the phenomenon. This effect could then be included using the Caldeira-Leggett dissipative tunneling effect [4].