Study of effects of confinement on vortex structure in dilute Bose-Einstein condensate

Abstract

In this thesis, I study the e ect of con nement on the core structure of vortex state in dilute Bose gases. Densely packed vortex lattice presents a possibility of observing many exotic phenomena like quantum melting and atomic quantum Hall states. One way to achieve such dense packing is to decrease vortex core width to allow accommodation of more vortices before the quantum melting transition. Con nement might play a key role in modulating vortex width below the conventional healing length limit. I have studied two di erent systems: 1) hard boundary con nement in the transverse direction with a xed far eld density, and 2) a weakly interacting gas in an axisymmetric harmonic trap and xed number of particles. In the rst case, calculations have been carried out in a mean eld approach. I observe that the vortex width near the centre of the trap scales as the con nement length when it is of the order of healing length. But this approach breaks down near the edges and requires further analysis. In the second system, both the length scales of con nement play a role in determining the core width which can be further reduced by making the interactions attractive. The minimum achievable vortex width for a xed trap depends on the strength of attractive interaction and the ratio of characteristic lengths in the transverse and radial direction.