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

Low-Lying Excitations from the Yrast Line of Weakly Interacting Trapped Bosons

Through an extensive numerical study, we find that the low-lying, quasi-degenerate eigenenergies of weakly-interacting trapped N bosons with total angular momentum L are given in case of small L/N and sufficiently small L by E = L hbar omega + g[N(N-L/2-1)+1.59 n(n-1)/2], where omega is the frequency of the trapping potential and g is the strength of the repulsive contact interaction; the last term arises from the pairwise repulsive interaction among n octupole excitations and describes the lowest-lying excitation spectra from the Yrast line. In this case, the quadrupole modes do not interact with themselves and, together with the octupole modes, exhaust the low-lying spectra which are separated from others by N-linear energy gaps.Comment: 5 pages, RevTeX, 2 figures, revised version, submitted to PR

Low-lying excitations of a trapped rotating Bose-Einstein condensate

We investigate the low-lying excitations of a weakly-interacting, harmonically-trapped Bose-Einstein condensed gas under rotation, in the limit where the angular mometum $L$ of the system is much less than the number of the atoms $N$ in the trap. We show that in the asymptotic limit $N \to \infty$ the excitation energy, measured from the energy of the lowest state, is given by $27 N_{3}(N_{3}-1) v_0 /68$, where $N_{3}$ is the number of octupole excitations and $v_{0}$ is the unit of the interaction energy.Comment: 3 pages, RevTex, 2 ps figures, submitted to PR

Operator-Algebraic Approach to the Yrast Spectrum of Weakly Interacting Trapped Bosons

We present an operator-algebraic approach to deriving the low-lying quasi-degenerate spectrum of weakly interacting trapped N bosons with total angular momentum \hbar L for the case of small L/N, demonstrating that the lowest-lying excitation spectrum is given by 27 g n_3(n_3-1)/34, where g is the strength of the repulsive contact interaction and n_3 the number of excited octupole quanta. Our method provides constraints for these quasi-degenerate many-body states and gives higher excitation energies that depend linearly on N.Comment: 7 pages, one figur

Anomalous rotational properties of Bose-Einstein condensates in asymmetric traps

We study the rotational properties of a Bose-Einstein condensate confined in a rotating harmonic trap for different trap anisotropies. Using simple arguments, we derive expressions for the velocity field of the quantum fluid for condensates with or without vortices. While the condensed gas describes open spiraling trajectories, on the frame of reference of the rotating trap the motion of the fluid is against the trap rotation. We also find explicit formulae for the angular momentum and a linear and Thomas-Fermi solutions for the state without vortices. In these two limits we also find an analytic relation between the shape of the cloud and the rotation speed. The predictions are supported by numerical simulations of the mean field Gross-Pitaevskii model.Comment: 4 RevTeX pages, 2 EPS figures; typos fixed, reference adde

Nonlinear dynamics for vortex lattice formation in a rotating Bose-Einstein condensate

We study the response of a trapped Bose-Einstein condensate to a sudden turn-on of a rotating drive by solving the two-dimensional Gross-Pitaevskii equation. A weakly anisotropic rotating potential excites a quadrupole shape oscillation and its time evolution is analyzed by the quasiparticle projection method. A simple recurrence oscillation of surface mode populations is broken in the quadrupole resonance region that depends on the trap anisotropy, causing stochastization of the dynamics. In the presence of the phenomenological dissipation, an initially irrotational condensate is found to undergo damped elliptic deformation followed by unstable surface ripple excitations, some of which develop into quantized vortices that eventually form a lattice. Recent experimental results on the vortex nucleation should be explained not only by the dynamical instability but also by the Landau instability; the latter is necessary for the vortices to penetrate into the condensate.Comment: RevTex4, This preprint includes no figures. You can download the complete article and figures at http://matter.sci.osaka-cu.ac.jp/bsr/cond-mat.htm

Dark soliton states of Bose-Einstein condensates in anisotropic traps

Dark soliton states of Bose-Einstein condensates in harmonic traps are studied both analytically and computationally by the direct solution of the Gross-Pitaevskii equation in three dimensions. The ground and self-consistent excited states are found numerically by relaxation in imaginary time. The energy of a stationary soliton in a harmonic trap is shown to be independent of density and geometry for large numbers of atoms. Large amplitude field modulation at a frequency resonant with the energy of a dark soliton is found to give rise to a state with multiple vortices. The Bogoliubov excitation spectrum of the soliton state contains complex frequencies, which disappear for sufficiently small numbers of atoms or large transverse confinement. The relationship between these complex modes and the snake instability is investigated numerically by propagation in real time.Comment: 11 pages, 8 embedded figures (two in color

Solitons, solitonic vortices, and vortex rings in a confined Bose-Einstein condensate

Quasi-one-dimensional solitons that may occur in an elongated Bose-Einstein condensate become unstable at high particle density. We study two basic modes of instability and the corresponding bifurcations to genuinely three-dimensional solitary waves such as axisymmetric vortex rings and non-axisymmetric solitonic vortices. We calculate the profiles of the above structures and examine their dependence on the velocity of propagation along a cylindrical trap. At sufficiently high velocity, both the vortex ring and the solitonic vortex transform into an axisymmetric soliton. We also calculate the energy-momentum dispersions and show that a Lieb-type mode appears in the excitation spectrum for all particle densities.Comment: RevTeX 9 pages, 9 figure

Generation and evolution of vortex-antivortex pairs in Bose-Einstein condensates

We propose a method for generating and controlling a spatially separated vortex--antivortex pair in a Bose-Einstein condensate trapped in a toroidal potential. Our simulations of the time dependent Gross-Pitaevskii equation show that in toroidal condensates vortex dynamics are different from the dynamics in the homogeneous case. Our numerical results agree well with analytical calculations using the image method. Our proposal offers an effective example of coherent generation and control of vortex dynamics in atomic condensates.Comment: 4 pages, 2 figure

Split vortices in optically coupled Bose-Einstein condensates

We study a rotating two-component Bose-Einstein condensate in which an optically induced Josephson coupling allows for population transfer between the two species. In a regime where separation of species is favored, the ground state of the rotating system displays domain walls with velocity fields normal to them. Such a configuration looks like a vortex split into two halves, with atoms circulating around the vortex and changing their internal state in a continuous way.Comment: 4 EPS pictures, 4 pages; Some errata have been corrected and thep resentation has been slightly revise