|Wednesday 8 March 10-11am ||CM219||Dr Hayder Salman, University of East Anglia||Threading Knotted and Tangled Filamentary Phase Defects in Complex Scalar Fields|
Experimental advances that have been made in recent years have made it increasingly possible to create matter wave fields in atomic Bose-Einstein condensates containing knotted or linked filamentary phase defects. These defects correspond to topological excitations in the form of quantized superfluid vortices. Knotted vortices have already been created and studied under controlled conditions in classical fluids. However, in these cases, vorticity acts to erode the vortical core of the vortices. An advantage of quantized superfluid vortices is that the vorticity remains concentrated along filaments throughout the dynamics. Nevertheless, quantum effects allow reconnections to occur that can change the topology of the fluid. This makes matter wave (as well as optical) fields an ideal setting in which to quantify helicity for topologically non-trivial vortex configurations. Although an excellent microscopic model exists to study the dynamics of such defects in superfluids, several challenges exist in generating an initial wavefunction containing knotted configurations. In this talk, I will show, using methods from differential geometry, how one can imprint any desired vortex configuration into the wavefunction. Using the imprinted fields, we perform numerical simulations of several knotted defects to illustrate their dynamical behaviour. I will also discuss the role of helicity for superfluid vortices.