Quantum number dimensional scaling analysis for excited states of multielectron atoms

A new dimensional scaling method for the calculation of excited states of multielectron atoms is introduced. By including the principle and orbital quantum numbers in the dimension parameter, we obtain an energy expression for excited states including high angular momentum states. The method is tested on He, Li, and Be. We obtain good agreement with more orthodox quantum mechanical treatments even in the zeroth order.Comment: Submitted to Physical Review A, 13 pages, 6 Table

Vortex energy and vortex bending for a rotating Bose-Einstein condensate

For a Bose-Einstein condensate placed in a rotating trap, we give a simplified expression of the Gross-Pitaevskii energy in the Thomas Fermi regime, which only depends on the number and shape of the vortex lines. Then we check numerically that when there is one vortex line, our simplified expression leads to solutions with a bent vortex for a range of rotationnal velocities and trap parameters which are consistent with the experiments.Comment: 7 pages, 2 figures. submitte

Unusual condensates in quark and atomic systems

In these lectures we discuss condensates which are formed in quark matter when it is squeezed and in a gas of fermionic atoms when it is cooled. The behavior of these two seemingly very different systems reveals striking similarities. In particular, in both systems the Bose-Einstein condensate to Bardeen--Cooper-Schrieffer (BEC-BCS) crossover takes place.Comment: Lectures delivered at 8th Moscow school of Physics (33rd ITEP Winter School of Physics

On the shape of vortices for a rotating Bose Einstein condensate

For a Bose-Einstein condensate placed in a rotating trap, we study the simplified energy of a vortex line derived in Aftalion-Riviere Phys. Rev. A 64, 043611 (2001) in order to determine the shape of the vortex line according to the rotational velocity and the elongation of the condensate. The energy reflects the competition between the length of the vortex which needs to be minimized taking into account the anisotropy of the trap and the rotation term which pushes the vortex along the z axis. We prove that if the condensate has the shape of a pancake, the vortex stays straight along the z axis while in the case of a cigar, the vortex is bent

Exact Eignstates for Trapped Weakly Interacting Bosons in Two Dimensions

A system of N two-dimensional weakly interacting bosons in a harmonic trap is considered. When the two-particle potential is a delta function Smith and Wilkin have analytically proved that the elementary symmetric polynomials of particle coordinates measured from the center of mass are exact eigenstates. In this study, we point out that their proof works equally well for an arbitrary two-particle potential which possesses the translational and rotational symmetries. We find that the interaction energy associated with the eigenstate with angular momentum L is equal to aN(N-1)/2+(b-a)NL/2, where a and b are the interaction energies of two bosons in the lowest-energy one-particle state with zero and one unit of angular momentum, respectively. Additionally, we study briefly the case of attractive quartic interactions. We prove rigorously that the lowest-energy state is the one in which all angular momentum is carried by the center of mass motion.Comment: 4 pages, minor changes made, to appear in PRA Brie

Dynamics of a Vortex in a Trapped Bose-Einstein Condensate

We consider a large condensate in a rotating anisotropic harmonic trap. Using the method of matched asymptotic expansions, we derive the velocity of an element of vortex line as a function of the local gradient of the trap potential, the line curvature and the angular velocity of the trap rotation. This velocity yields small-amplitude normal modes of the vortex for 2D and 3D condensates. For an axisymmetric trap, the motion of the vortex line is a superposition of plane-polarized standing-wave modes. In a 2D condensate, the planar normal modes are degenerate, and their superposition can result in helical traveling waves, which differs from a 3D condensate. Including the effects of trap rotation allows us to find the angular velocity that makes the vortex locally stable. For a cigar-shape condensate, the vortex curvature makes a significant contribution to the frequency of the lowest unstable normal mode; furthermore, additional modes with negative frequencies appear. As a result, it is considerably more difficult to stabilize a central vortex in a cigar-shape condensate than in a disc-shape one. Normal modes with imaginary frequencies can occur for a nonaxisymmetric condensate (in both 2D and 3D). In connection with recent JILA experiments, we consider the motion of a straight vortex line in a slightly nonspherical condensate. The vortex line changes its orientation in space at the rate proportional to the degree of trap anisotropy and can exhibit periodic recurrences.Comment: 19 pages, 6 eps figures, REVTE

Coherent Dynamics of Vortex Formation in Trapped Bose-Einstein Condensates

Simulations of a rotationally stirred condensate show that a regime of simple behaviour occurs in which a single vortex cycles in and out of the condensate. We present a simple quantitative model of this behaviour, which accurately describes the full vortex dynamics, including a critical angular speed of stirring for vortex formation. A method for experimentally preparing a condensate in a central vortex state is suggested.Comment: 4 pages, 4 figures, REVTeX 3.1; Submitted to Physical Review Letters (5 February 1999); See http://www.physics.otago.ac.nz/research/bec/vortex for MPEG movies and further information; Accepted for Physical Review Letters (24 June 1999); Changes: updated Figs 1 and 2 (new style), minor typos fixed, more discussion at en

Modification of radiation pressure due to cooperative scattering of light

Cooperative spontaneous emission of a single photon from a cloud of N atoms modifies substantially the radiation pressure exerted by a far-detuned laser beam exciting the atoms. On one hand, the force induced by photon absorption depends on the collective decay rate of the excited atomic state. On the other hand, directional spontaneous emission counteracts the recoil induced by the absorption. We derive an analytical expression for the radiation pressure in steady-state. For a smooth extended atomic distribution we show that the radiation pressure depends on the atom number via cooperative scattering and that, for certain atom numbers, it can be suppressed or enhanced.Comment: 8 pages, 2 Figure

Rotational Dynamics of Vortices in Confined Bose-Einstein Condensates

We derive the frequency of precession and conditions for stability for a quantized vortex in a single-component and a two-component Bose-Einstein condensate. The frequency of precession is proportional to the gradient of the free energy with respect to displacement of the vortex core. In a two-component system, it is possible to achieve a local minimum in the free energy at the center of the trap. The presence of such a minimum implies the existence of a region of energetic stability where the vortex cannot escape and where one may be able to generate a persistent current.Comment: 6 Pages, 6 Figure

Detection of vorticity in Bose-Einstein condensed gases by matter-wave interference

A phase-slip in the fringes of an interference pattern is an unmistakable characteristic of vorticity. We show dramatic two-dimensional simulations of interference between expanding condensate clouds with and without vorticity. In this way, vortices may be detected even when the core itself cannot be resolved.Comment: 3 pages, RevTeX, plus 6 PostScript figure