Construction of a giant vortex state in a trapped Fermi system

A superfluid atomic Fermi system may support a giant vortex if the trapping potential is anharmonic. In such a potential, the single-particle spectrum has a positive curvature as a function of angular momentum. A tractable model is put up in which the lowest and next lowest Landau levels are occupied. Different parameter regimes are identified and characterized. Due to the dependence of the interaction on angular momentum quantum number, the Cooper pairing is at its strongest not only close to the Fermi level, but also close to the energy minimum. It is shown that the gas is superfluid in the interior of the toroidal density distribution and normal in the outer regions. Furthermore, the pairing may give rise to a localized density depression in configuration space.Comment: 12 pages, 14 figure file

Stability of the solutions of the Gross-Pitaevskii equation

We examine the static and dynamic stability of the solutions of the Gross-Pitaevskii equation and demonstrate the intimate connection between them. All salient features related to dynamic stability are reflected systematically in static properties. We find, for example, the obvious result that static stability always implies dynamic stability and present a simple explanation of the fact that dynamic stability can exist even in the presence of static instability.Comment: 7 pages, 1 figur

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

The Surface of a Bose-Einstein Condensed Atomic Cloud

We investigate the structure and collective modes of a planar surface of a trapped Bose-Einstein condensed gas at zero temperature. In the long-wavelength limit we find a mode similar to the gravity wave on the surface of a fluid with the frequency $\omega$ and the wavenumber $q$ related by $\omega^2=Fq/m$. Here $F$ is the force due to the confining potential at the surface and $m$ is the particle mass. At shorter wavelengths we use a variational approach and find corrections to $\omega^2$ of order $q^4 \ln{q}$. We demonstrate the usefulness of the concept of an effective surface tension for describing both static and dynamic properties of condensed atomic clouds.Comment: 8 pages, REVTEX, submitted to Phys. Rev.

Ansatz from Non-Linear Optics Applied to Trapped Bose-Einstein Condensates

A simple analytical ansatz, which has been used to describe the intensity profile of the similariton laser (a laser with self-similar propagation of ultrashort pulses), is used as a variational wave function to solve the Gross-Pitaevskii equation for a wide range of interaction parameters. The variational form interpolates between the noninteracting density profile and the strongly interacting Thomas-Fermi profile smoothly. The simple form of the ansatz is modified for both cylindrically symmetric and completely anisotropic harmonic traps. The resulting ground-state density profile and energy are in very good agreement with both the analytical solutions in the limiting cases of interaction and the numerical solutions in the intermediate regime.Comment: 4 pages, 3 figures, published versio

Superfluid-Insulator transition of ultracold atoms in an optical lattice in the presence of a synthetic magnetic field

We study the Mott insulator-superfluid transition of ultracold bosonic atoms in a two-dimensional square optical lattice in the presence of a synthetic magnetic field with p/q (p and q being co-prime integers) flux quanta passing through each lattice plaquette. We show that on approach to the transition from the Mott side, the momentum distribution of the bosons exhibits q precursor peaks within the first magnetic Brillouin zone. We also provide an effective theory for the transition and show that it involves q interacting boson fields. We construct, from a mean-field analysis of this effective theory, the superfluid ground states near the transition and compute, for q=2,3, both the gapped and the gapless collective modes of these states. We suggest experiments to test our theory.Comment: 4 pages, 4 figs; v

Multiply quantized vortices in trapped Bose-Einstein condensates

Vortex configurations in rotating Bose-Einstein condensed gases trapped in power-law and anharmonic potentials are studied. When the confining potential is steeper than harmonic in the plane perpendicular to the axis of rotation, vortices with quantum numbers larger than one are energetically favorable if the interaction is weak enough. Features of the wave function for small and intermediate rotation frequencies are investigated numerically.Comment: 9 pages, 6 figures. Revised and extended article following referee repor

Laser-driven plasma waves in capillary tubes

The excitation of plasma waves over a length of up to 8 centimeters is, for the first time, demon- strated using laser guiding of intense laser pulses through hydrogen filled glass capillary tubes. The plasma waves are diagnosed by spectral analysis of the transmitted laser radiation. The dependence of the spectral redshift, measured as a function of filling pressure, capillary tube length and incident laser energy, is in excellent agreement with simulation results. The longitudinal accelerating field inferred from the simulations is in the range 1 -10 GV/m

Betatron emission as a diagnostic for injection and acceleration mechanisms in laser-plasma accelerators

Betatron x-ray emission in laser-plasma accelerators is a promising compact source that may be an alternative to conventional x-ray sources, based on large scale machines. In addition to its potential as a source, precise measurements of betatron emission can reveal crucial information about relativistic laser-plasma interaction. We show that the emission length and the position of the x-ray emission can be obtained by placing an aperture mask close to the source, and by measuring the beam profile of the betatron x-ray radiation far from the aperture mask. The position of the x-ray emission gives information on plasma wave breaking and hence on the laser non-linear propagation. Moreover, the measurement of the longitudinal extension helps one to determine whether the acceleration is limited by pump depletion or dephasing effects. In the case of multiple injections, it is used to retrieve unambiguously the position in the plasma of each injection. This technique is also used to study how, in a capillary discharge, the variations of the delay between the discharge and the laser pulse affect the interaction. The study reveals that, for a delay appropriate for laser guiding, the x-ray emission only occurs in the second half of the capillary: no electrons are injected and accelerated in the first half.Comment: 8 pages, 6 figures. arXiv admin note: text overlap with arXiv:1104.245