N. K. Wilkin

Quantum Phases of Vortices in Rotating Bose-Einstein Condensates

We investigate the ground states of weakly interacting bosons in a rotating trap as a function of the number of bosons, N, and the average number of vortices, N(V). We identify the filling fraction nu identical with N/N(V) as the parameter controlling the nature of these states. We present results indicating that, as a function of nu, there is a zero temperature phase transition between a triangular vortex lattice phase, and strongly correlated vortex liquid phases. The vortex liquid phases appear to be the Read-Rezayi parafermion states.

Condensation of 'Composite Bosons' in a Rotating BEC

We provide evidence for several novel phases in the dilute limit of rotating Bose-Einstein condensates. By exact calculation of wave functions and energies for small numbers of particles, we show that the states near integer angular momentum per particle are best considered condensates of composite entities, involving vortices and atoms. We are led to this result by explicit comparison with a description purely in terms of vortices. Several parallels with the fractional quantum Hall effect emerge, including the presence of the Pfaffian state.

Exact eigenstates for repulsive bosons in two dimensions

We consider a model of N two-dimensional bosons in a harmonic potential with weak repulsive \ensuremath{\delta}-function interactions. We show analytically that, for angular momentum

Exact Vortex Nucleation and Cooperative Vortex Tunneling in Dilute Bose-Einstein Condensates

Ll~N,

Disorder Driven Destruction of a Phase Transition in the Vortex System of a Superconductor

the elementary symmetric polynomials of particle coordinates measured from the center of mass are exact eigenstates with energy

Decoupling and melting in a layered superconductor

N(N\ensuremath{-}L/2\ensuremath{-}1).

ENERGY COST ASSOCIATED WITH VORTEX CROSSING IN SUPERCONDUCTORS

Extensive numerical analysis confirms that these are actually the ground states, but we are currently unable to prove this analytically. The special case

Vortices and collective excitations in rotating BECs

L=N

The Effect of Disorder on Melting and Decoupling Transitions in Layered Superconductors

can be thought of as the generalization of the usual superfluid one-vortex state to Bose-Einstein condensates in a trap.

PLASTIC ENERGIES IN LAYERED SUPERCONDUCTORS

With the imminent advent of mesoscopic rotating Bose-Einstein condensates in the lowest Landau level regime, we explore lowest Landau level vortex nucleation. An exact many-body analysis is presented in a weakly elliptical trap for up to 400 particles. Striking non-mean-field features are exposed at filling factors >>1. For example, near the critical rotation frequency pairs of energy levels approach each other with exponential accuracy. A physical interpretation is provided by requantizing a mean-field theory, where 1/N plays the role of Plancks constant, revealing two vortices cooperatively tunneling between classically degenerate energy minima. The tunnel splitting variation is described in terms of frequency, particle number, and ellipticity.