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.
