Vortices in Bose-Einstein-Condensed Atomic Clouds

The properties of vortex states in a Bose-Einstein condensed cloud of atoms are considered at zero temperature. Using both analytical and numerical methods we solve the time-dependent Gross-Pitaevskii equation for the case when a cloud of atoms containing a vortex is released from a trap. In two dimensions we find the simple result that the time dependence of the cloud radius is given by $(1+\omega^2t^2)^{1/2}$, where $\omega$ is the trap frequency. We calculate and compare the expansion of the vortex core and the cloud radius for different numbers of particles and interaction strengths, in both two and three dimensions, and discuss the circumstances under which vortex states may be observed experimentally.Comment: Revtex, 11 pages including 5 eps figures, submitted to Phys. Rev. A; new reference added, remark added in Sec. IIIB, axis label added in Fig.

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

Presynaptic actions of 4-Aminopyridine and γ-aminobutyric acid on rat sympathetic ganglia in vitro

Responses to bath-applications of 4-aminopyridine (4-AP) and -aminobutyric acid (GABA) were recorded intracellularly from neurones in the rat isolated superior cervical ganglion. 4-aminopyridine (0.1–1.0 mmol/l) usually induced spontaneous action potentials and excitatory postsynaptic potentials (EPSPs), which were blocked by hexamethonium. Membrane potential was unchanged; spike duration was slightly increased. Vagus nerve B-and C-fibre potentials were prolonged. In 4-AP solution (0.1–0.3 mmol/l), GABA (0.1 mmol/l), 3-aminopropanesulphonic acid or muscimol evoked bursts of spikes and EPSPs in addition to a neuronal depolarization. These bursts, which were not elicited by glycine, glutamate, taurine or (±)-baclofen, were completely antagonised by hexamethonium, tetrodotoxin or bicuculline methochloride. It is concluded that: (a) 4-AP has a potent presynaptic action on sympathetic ganglia; (b) presynaptic actions of GABA can be recorded postsynaptically in the presence of 4-AP; and (c) the presynaptic GABA-receptors revealed in this condition are similar to those on the postsynaptic membrane

Bose-Einstein condensation in variable dimensionality

We introduce dimensional perturbation techniques to Bose-Einstein condensation of inhomogeneous alkali gases (BEC). The perturbation parameter is delta=1/kappa, where kappa depends on the effective dimensionality of the condensate and on the angular momentum quantum number. We derive a simple approximation that is more accurate and flexible than the N -> infinity Thomas-Fermi ground state approximation (TFA) of the Gross-Pitaevskii equation. The approximation presented here is well-suited for calculating properties of states in three dimensions and in low effective dimensionality, such as vortex states in a highly anisotropic trap

Phase diagram of quantized vortices in a trapped Bose-Einstein condensed gas

We investigate the thermodynamic stability of quantized vortices in a dilute Bose gas confined by a rotating harmonic trap at finite temperature. Interatomic forces play a crucial role in characterizing the resulting phase diagram, especially in the large $N$ Thomas-Fermi regime. We show that the critical temperature for the creation of stable vortices exhibits a maximum as a function of the frequency of the rotating trap and that the corresponding transition is associated with a discontinuity in the number of atoms in the condensate. Possible strategies for approaching the vortical region are discussed.Comment: Revtex, 4 pages, 2 figure

Free expansion of two-dimensional condensates with a vortex

We study the free expansion of a pancake-shaped Bose-condensed gas, which is initially trapped under harmonic confinement and containing a vortex at its centre. In the case of a radial expansion holding fixed the axial confinement we consider various models for the interactions, depending on the thickness of the condensate relative to the value of the scattering length. We are thus able to evaluate different scattering regimes ranging from quasi-three-dimensional (Q3D) to strictly two-dimensional (2D). We find that as the system goes from Q3D to 2D the expansion rate of the condensate increases whereas that of the vortex core decreases. In the Q3D scattering regime we also examine a fully free expansion in 3D and find oscillatory behaviour for the vortex core radius: an initial fast expansion of the vortex core is followed by a slowing down. Such a nonuniform expansion rate of the vortex core may be taken into account in designing new experiments.Comment: 10 pages, 4 figure

Stability of a vortex in a small trapped Bose-Einstein condensate

A second-order expansion of the Gross-Pitaevskii equation in the interaction parameter determines the thermodynamic critical angular velocity Omega_c for the creation of a vortex in a small axisymmetric condensate. Similarly, a second-order expansion of the Bogoliubov equations determines the (negative) frequency omega_a of the anomalous mode. Although Omega_c = -omega_a through first order, the second-order contributions ensure that the absolute value |omega_a| is always smaller than the critical angular velocity Omega_c. With increasing external rotation Omega, the dynamical instability of the condensate with a vortex disappears at Omega*=|omega_a|, whereas the vortex state becomes energetically stable at the larger value Omega_c. Both second-order contributions depend explicitly on the axial anisotropy of the trap. The appearance of a local minimum of the free energy for a vortex at the center determines the metastable angular velocity Omega_m. A variational calculation yields Omega_m=|\omega_a| to first order (hence Omega_m also coincides with the critical angular velocity Omega_c to this order). Qualitatively, the scenario for the onset of stability in the weak-coupling limit is the same as that found in the strong-coupling (Thomas-Fermi) limit.Comment: 8 pages, RevTe

Perfectionism and achievement goals in young Finnish ice-hockey players aspiring to make the Under-16 national team

Research on perfectionism suggests that is it useful to differentiate between perfectionistic strivings and perfectionistic concerns. Regarding the 2 x 2 achievement goal framework, the usefulness of this differentiation was recently demonstrated in a study with university student athletes (Stoeber, Stoll, Pescheck, & Otto, 2008, Study 2), in which it was found that perfectionistic strivings were associated with mastery-approach and performance-approach goals and perfectionistic concerns with mastery-avoidance, performance-approach, and performance-avoidance goals. Because the study was largely exploratory and only used non-elite athletes, the aim of the present research was to replicate and extend these findings by investigating a sample of 138 young, elite ice-hockey players, while adding further measures of perfectionism and using structural equation modelling (SEM) to confirm the relationships between perfectionistic strivings, perfectionistic concerns,and the 2 x 2 achievement goals. The SEM results showed that, in elite athletes also, perfectionistic strivings are associated with mastery-approach and performance-approach goals, whereas perfectionistic concerns are associated with masteryavoidance, performance-approach, and performance-avoidance goals. Our findings corroborate the importance of differentiating between perfectionistic strivings and perfectionistic concerns when studying perfectionism in sports, because only perfectionistic concerns (and not perfectionistic strivings) are associated with maladaptive patterns of achievement goals

Creation of a monopole in a spinor condensate

We propose a method to create a monopole structure in a spin-1 spinor condensate by applying the basic methods used to create vortices and solitons experimentally in single-component condensates. We show, however, that by using a two-component structure for a monopole, we can simplify our proposed experimental approach and apply it also to ferromagnetic spinor condensates. We also discuss the observation and dynamics of such a monopole structure, and note that the dynamics of the two-component monopole differs from the dynamics of the three-component monopole.Comment: The focus of the paper is shifted towards creation and observation of monopole

An Atom Laser with a cw Output Coupler

We demonstrate a continuous output coupler for magnetically trapped atoms. Over a period of up to 100 ms a collimated and monoenergetic beam of atoms is continuously extracted from a Bose- Einstein condensate. The intensity and kinetic energy of the output beam of this atom laser are controlled by a weak rf-field that induces spin flips between trapped and untrapped states. Furthermore, the output coupler is used to perform a spectroscopic measurement of the condensate, which reveals the spatial distribution of the magnetically trapped condensate and allows manipulation of the condensate on a micrometer scale.Comment: 4 pages, 4 figure