Transitions between phyllotactic lattice states in curved geometries.

Phyllotaxis, the regular arrangement of leaves or other lateral organs in plants including pineapples, sunflowers and some cacti, has attracted scientific interest for centuries. More recently there has been interest in phyllotaxis within physical systems, especially for cylindrical geometry. In this letter, we expand from a cylindrical geometry and investigate transitions between phyllotactic states of soft vortex matter confined to a conical frustum. We show that the ground states of this system are consistent with previous results for cylindrical confinement and discuss the resulting defect structures at the transitions. We then eliminate these defects from the system by introducing a density gradient to create a configuration in a single state. The nature of the density gradient limits this approach to a small parameter range on the conical system. We therefore seek a new surface, the horn, for which a defect-free state can be maintained for a larger range of parameters.

Exact vortex nucleation and cooperative vortex tunneling in dilute Bose-Einstein condensates.

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 Planck's 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.

Anomalous hydrodynamics and normal fluids in rapidly rotating Bose-Einstein condensates.

In rapidly rotating condensed Bose systems we show that there is a regime of anomalous hydrodynamics which coincides with the mean field quantum Hall regime. A consequence is the absence of a normal fluid in any conventional sense. However, even the superfluid hydrodynamics is not described by conventional Bernoulli and continuity equations. We show that there are constraints which connect spatial variations of density and phase and that the vortex positions are not the simplest description of the dynamics. We demonstrate, inter alia, a simple relation between vortices and surface waves. We show that the surface waves can emulate a "normal fluid," allowing dissipation by energy and angular momentum absorbtion from vortex motion in the trap. The time scale is sensitive to the initial configuration, which can lead to long-lived vortex patches--perhaps related to those observed at JILA.

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.