Spin textures in rotating two-component Bose-Einstein condensates

We investigate two kinds of coreless vortices with axisymmetric and nonaxisymmetric configurations in rotating two-component Bose-Einstein condensates. Starting from the Gross-Pitaevskii energy functional in a rotating frame, we derive a nonlinear sigma model generalized to the two-component condensates. In terms of a pseudospin representation, an axisymmetric vortex and a nonaxisymmetric one correspond to spin textures referred to as a "skyrmion" and a "meron-pair", respectively. A variational method is used to investigate the dependence of the sizes of the stable spin textures on system parameters, and the optimized variational function is found to reproduce well the numerical solution. In the SU(2) symmetric case, the optimal skyrmion and meron-pair are degenerate and transform to each other by a rotation of the pseudospin. An external rf-field that couples coherently the hyperfine states of two components breaks the degeneracy in favor of the meron-pair texture due to an effective transverse pseudomagnetic field. The difference between the intracomponent and intercomponent interactions yields a longitudinal pseudomagnetic field and a ferromagnetic or an antiferromagnetic pseudospin interaction, leading to a meron-pair texture with an anisotropic distribution of vorticity.Comment: 14 pages, 15 figure

Symmetry and inert states of spin Bose Condensates

We construct the list of all possible inert states of spin Bose condensates for $S \le 4$. In doing so, we also obtain their symmetry properties. These results are applied to classify line defects of these spin condensates at zero magnetic field.Comment: an error in Sec III C correcte

Studies of the 1^{1}S0_{0}--3^3P0_0 transition in atomic ytterbium for optical clocks and qubit arrays

We report an observation of the weak $6^{1}$S$_{0}$-$6^3$P$_0$ transition in $^{171,173}$Yb as an important step to establish Yb as a primary candidate for future optical frequency standards, and to open up a new approach for qubits using the $^{1}$S$_{0}$ and $^3$P$_0$ states of Yb atoms in an optical lattice.Comment: 5 pages, 3 figure

Microscopic theory of atom-molecule oscillations in a Bose-Einstein condensate

In a recent experiment at JILA [E.A. Donley et al., Nature (London) 417, 529 (2002)] an initially pure condensate of Rb-85 atoms was exposed to a specially designed time dependent magnetic field pulse in the vicinity of a Feshbach resonance. The production of new components of the gas as well as their oscillatory behavior have been reported. We apply a microscopic theory of the gas to identify these components and determine their physical properties. Our time dependent studies allow us to explain the observed dynamic evolution of all fractions, and to identify the physical relevance of the pulse shape. Based on ab initio predictions, our theory strongly supports the view that the experiments have produced a molecular condensate.Comment: 18 pages, 20 figure

Laser frequency stabilization to a single ion

A fundamental limit to the stability of a single-ion optical frequency standard is set by quantum noise in the measurement of the internal state of the ion. We discuss how the interrogation sequence and the processing of the atomic resonance signal can be optimized in order to obtain the highest possible stability under realistic experimental conditions. A servo algorithm is presented that stabilizes a laser frequency to the single-ion signal and that eliminates errors due to laser frequency drift. Numerical simulations of the servo characteristics are compared to experimental data from a frequency comparison of two single-ion standards based on a transition at 688 THz in 171Yb+. Experimentally, an instability sigma_y(100 s)=9*10^{-16} is obtained in the frequency difference between both standards.Comment: 15 pages, 5 figures, submitted to J. Phys.

Strongly enhanced inelastic collisions in a Bose-Einstein condensate near Feshbach resonances

The properties of Bose-Einstein condensed gases can be strongly altered by tuning the external magnetic field near a Feshbach resonance. Feshbach resonances affect elastic collisions and lead to the observed modification of the scattering length. However, as we report here, this is accompanied by a strong increase in the rate of inelastic collisions. The observed three-body loss rate in a sodium Bose-Einstein condensation increased when the scattering length was tuned to both larger or smaller values than the off-resonant value. This observation and the maximum measured increase of the loss rate by several orders of magnitude are not accounted for by theoretical treatments. The strong losses impose severe limitations for using Feshbach resonances to tune the properties of Bose-Einstein condensates. A new Feshbach resonance in sodium at 1195 G was observed.Comment: 4 pages, 3 figure

Effect of Quadratic Zeeman Energy on the Vortex of Spinor Bose-Einstein Condensates

The spinor Bose-Einstein condensate of atomic gases has been experimentally realized by a number of groups. Further, theoretical proposals of the possible vortex states have been sugessted. This paper studies the effects of the quadratic Zeeman energy on the vortex states. This energy was ignored in previous theoretical studies, although it exists in experimental systems. We present phase diagrams of various vortex states taking into account the quadratic Zeeman energy. The vortex states are calculated by the Gross-Pitaevskii equations. Several new kinds of vortex states are found. It is also found that the quadratic Zeeman energy affects the direction of total magnetization and causes a significant change in the phase diagrams.Comment: 6 pages, 5 figures. Published in J. Phys. Soc. Jp

Phase separation of Bose-Einstein condensates

The zero-temperature system of two dilute overlapping Bose-Einstein condensates is unstable against long wavelength excitations if the interaction strength between the distinguishable bosons exceeds the geometric mean of the like-boson interaction strengths. If the condensates attract each other, the instability is similar to the instability of the negative scattering length condensates. If the condensates repel, they separate spatially into condensates of equal pressure. We estimate the boundary size, surface tension and energy of the phase separated condensate system and we discuss the implications for double condensates in atomic traps.Comment: 11 pages, 1 figur

Bose-Einstein condensation in shallow traps

In this paper we study the properties of Bose-Einstein condensates in shallow traps. We discuss the case of a Gaussian potential, but many of our results apply also to the traps having a small quadratic anharmonicity. We show the errors introduced when a Gaussian potential is approximated with a parabolic potential, these errors can be quite large for realistic optical trap parameter values. We study the behavior of the condensate fraction as a function of trap depth and temperature and calculate the chemical potential of the condensate in a Gaussian trap. Finally we calculate the frequencies of the collective excitations in shallow spherically symmetric and 1D traps.Comment: 6 pages, 4 figure