Rapidly rotating Bose-Einstein condensates in an anharmonic confinement

We examine a rapidly rotating Bose-Einstein condensate in an anharmonic confinement and find that many properties such as the critical rotating frequency and phase diagram are quite different from those in a harmonic trap. We investigate the phase transitions by means of average-vortex-approximation. We find that the vortex lattice consists of a vortex array with a hole in the center of the cloud as the rotating frequency $\Omega$ increases and the vortex becomes invisible when $\Omega$ reaches some value.Comment: Revtex, 5 pages, 2 figure

Dynamical evolution of a doubly-quantized vortex imprinted in a Bose-Einstein Condensate

The recent experiment by Y. Shin \emph{et al.} [Phys. Rev. Lett. \textbf{93}, 160406 (2004)] on the decay of a doubly quantized vortex imprinted in $^{23}$Na condensates is analyzed by numerically solving the Gross-Pitaevskii equation. Our results, which are in very good quantitative agreement with the experiment, demonstrate that the vortex decay is mainly a consequence of dynamical instability. Despite apparent contradictions, the local density approach is consistent with the experimental results. The monotonic increase observed in the vortex lifetimes is a consequence of the fact that, for large condensates, the measured lifetimes incorporate the time it takes for the initial perturbation to reach the central slice. When considered locally, the splitting occurs approximately at the same time in every condensate, regardless of its size.Comment: 5 pages, 4 figure

Vortex-Peierls States in Optical Lattices

We show that vortices, induced in cold atom superfluids in optical lattices, may order in a novel vortex-Peierls ground state. In such a state vortices do not form a simple lattice but arrange themselves in clusters, within which the vortices are partially delocalized, tunneling between classically degenerate configurations. We demonstrate that this exotic quantum many-body state is selected by an order-from-disorder mechanism for a special combination of the vortex filling and lattice geometry that has a macroscopic number of classically degenerate ground states.Comment: 4 pages, 4 figures. Published versio

Giant vortices in combined harmonic and quartic traps

We consider a rotating Bose-Einstein condensate confined in combined harmonic and quartic traps, following recent experiments [V. Bretin, S. Stock, Y. Seurin and J. Dalibard, cond-mat/0307464]. We investigate numerically the behavior of the wave function which solves the three-dimensional Gross Pitaevskii equation. When the harmonic part of the potential is dominant, as the angular velocities $Omega$ increases, the vortex lattice evolves into a giant vortex. We also investigate a case not covered by the experiments or the previous numerical works: for strong quartic potentials, the giant vortex is obtained for lower $Omega$, before the lattice is formed. We analyze in detail the three dimensional structure of vortices

Phase Separation of a Fast Rotating Boson-Fermion Mixture in the Lowest-Landau-Level Regime

By minimizing the coupled mean-field energy functionals, we investigate the ground-state properties of a rotating atomic boson-fermion mixture in a two-dimensional parabolic trap. At high angular frequencies in the mean-field-lowest-Landau-level regime, quantized vortices enter the bosonic condensate, and a finite number of degenerate fermions form the maximum-density-droplet state. As the boson-fermion coupling constant increases, the maximum density droplet develops into a lower-density state associated with the phase separation, revealing characteristics of a Landau-level structure

Incompressible liquid state of rapidly-rotating bosons at filling factor 3/2

Bosons in the lowest Landau level, such as rapidly-rotating cold trapped atoms, are investigated numerically in the specially interesting case in which the filling factor (ratio of particle number to vortex number) is 3/2. When a moderate amount of a longer-range (e.g. dipolar) interaction is included, we find clear evidence that the ground state is in a phase constructed earlier by two of us, in which excitations possess non-Abelian statistics.Comment: 5 pages, 5 figure

Energy gaps and roton structure above the nu=1/2 Laughlin state of a rotating dilute Bose-Einstein condensate

Exact diagonalization study of a rotating dilute Bose-Einstein condensate reveals that as the first vortex enters the system the degeneracy of the low-energy yrast spectrum is lifted and a large energy gap emerges. As more vortices enter with faster rotation, the energy gap decreases towards zero, but eventually the spectrum exhibits a rotonlike structure above the nu=1/2 Laughlin state without having a phonon branch despite the short-range nature of the interaction.Comment: 4 pages, 4 figures, 1 tabl

Phases of a rotating Bose-Einstein condensate with anharmonic confinement

We examine an effectively repulsive Bose-Einstein condensate of atoms that rotates in a quadratic-plus-quartic potential. With use of a variational method we identify the three possible phases of the system (multiple quantization, single quantization, and a mixed phase) as a function of the rotational frequency of the gas and of the coupling constant. The derived phase diagram is shown to be universal and the continuous transitions to be exact in the limit of weak coupling and small anharmonicity. The variational results are found to be consistent with numerical solutions of the Gross-Pitaevskii equation.Comment: 8 pages, 6 figure

Dissociation and Decay of Ultra-cold Sodium Molecules

The dissociation of ultracold molecules is studied by ramping an external magnetic field through a Feshbach resonance. The observed dissociation energy shows non-linear dependence on the ramp speed and directly yields the strength of the atom-molecule coupling. In addition, inelastic molecule-molecule and molecule-atom collisions are characterized

Novel ground states of Bose-condensed gases

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Physics, February 2005.Includes bibliographical references (leaves 131-142).Bose-Einstein condensates (BEC) provide a novel tool for the study of macroscopic quantum phenomena and condensed matter systems. Two of the recent frontiers, quantized vortices and ultracold molecules, are the subject of this thesis. The formation of highly-ordered vortex lattices in a Bose-condensed gas has been observed. These triangular lattices contain more than 150 vortices with lifetimes of several seconds. The vortices were generated by rotating the condensate with a scanning blue-detuned laser beam. Depending on the stirrer size, vortices were either nucleated at discrete surface-mode resonances (large beams) or over a broad range of stirring frequencies (small beams). Additionally, the dynamics of the lattices have been studied at finite temperature by varying the condensed fraction of atoms in the system. The decay of angular momentum is observed to be strongly temperature-dependant, while the crystallization of the lattice appears to be insensitive to temperature change. Recently, the field of BEC has been extended to include cold molecules. Here ultra-cold sodium molecules were produced from an atomic BEC by ramping an applied magnetic field across a Feshbach resonance. These molecules were used to demonstrate coherent molecular optics. In particular, we have extended Kapitza-Dirac and Bragg diffraction to cold molecules. By measuring the Bragg spectrum of the molecules immediately after their creation, the conversion from atoms to molecules was shown to be coherent - the matter wave analog to frequency doubling in optics. In addition, the more general process of sum-frequency generation was demonstrated.(cont.) Atoms prepared in two momentum states, prior to creating molecules, were observed to cross-pair, generating a third momentum state. Finally, molecular matter-wave interference was realized using an autocorrelation technique.by Jamil R. Abo-Shaeer.Ph.D