Three-dimensional vortex structure of a fast rotating Bose-Einstein condensate with harmonic-plus-quartic confinement

We address the challenging proposition of using real experimental parameters in a three-dimensional numerical simulation of fast rotating Bose-Einstein condensates. We simulate recent experiments [V. Bretin, S. Stock, Y. Seurin and J. Dalibard, Phys. Rev. Lett. 92, 050403 (2004); S. Stock, V. Bretin, S. Stock, F. Chevy and J. Dalibard, Europhys. Lett. 65, 594 (2004)] using an anharmonic (quadratic-plus-quartic) confining potential to reach rotation frequencies ($\Omega$) above the trap frequency ($\omega_\perp$). Our numerical results are obtained by propagating the 3D Gross-Pitaevskii equation in imaginary time. For $\Omega \leq\omega_\perp$, we obtain an equilibrium vortex lattice similar (as size and number of vortices) to experimental observations. For $\Omega>\omega_\perp$ we observe the evolution of the vortex lattice into an array of vortices with a central hole. Since this evolution was not visible in experiments, we investigate the 3D structure of vortex configurations and 3D-effects on vortex contrast. Numerical data are also compared to recent theory [D. E. Sheehy and L. Radzihovsky, Phys. Rev. A 70, 063620 (2004)] describing vortex lattice inhomogeneities and a remarkably good agreement is found.Comment: to appear in Phys Rev A 71 (2005

Spontaneous Dissociation of 85Rb Feshbach Molecules

The spontaneous dissociation of 85Rb dimers in the highest lying vibrational level has been observed in the vicinity of the Feshbach resonance which was used to produce them. The molecular lifetime shows a strong dependence on magnetic field, varying by three orders of magnitude between 155.5 G and 162.2 G. Our measurements are in good agreement with theoretical predictions in which molecular dissociation is driven by inelastic spin relaxation. Molecule lifetimes of tens of milliseconds can be achieved close to resonance.Comment: 4 pages, 3 figure

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

Ultracold Molecule Production Via a Resonant Oscillating Magnetic Field

A novel atom-molecule conversion technique has been investigated. Ultracold 85Rb atoms sitting in a dc magnetic field near the 155 G Feshbach resonance are associated by applying a small sinusoidal oscillation to the magnetic field. There is resonant atom to molecule conversion when the modulation frequency closely matches the molecular binding energy. We observe that the atom to molecule conversion efficiency depends strongly on the frequency, amplitude, and duration of the applied modulation and on the phase space density of the sample. This technique offers high conversion efficiencies without the necessity of crossing or closely approaching the Feshbach resonance and allows precise spectroscopic measurements. Efficiencies of 55% have been observed for pure Bose-Einstein condensates

Theory of vortex-lattice melting in a one-dimensional optical lattice

We investigate quantum and temperature fluctuations of a vortex lattice in a one-dimensional optical lattice. We discuss in particular the Bloch bands of the Tkachenko modes and calculate the correlation function of the vortex positions along the direction of the optical lattice. Because of the small number of particles in the pancake Bose-Einstein condensates at every site of the optical lattice, finite-size effects become very important. Moreover, the fluctuations in the vortex positions are inhomogeneous due to the inhomogeneous density. As a result, the melting of the lattice occurs from the outside inwards. However, tunneling between neighboring pancakes substantially reduces the inhomogeneity as well as the size of the fluctuations. On the other hand, nonzero temperatures increase the size of the fluctuations dramatically. We calculate the crossover temperature from quantum melting to classical melting. We also investigate melting in the presence of a quartic radial potential, where a liquid can form in the center instead of at the outer edge of the pancake Bose-Einstein condensates.Comment: 17 pages, 17 figures, submitted to Phys. Rev. A, references update

Spontaneous squeezing of a vortex in an optical lattice

We study the equilibrium states of a vortex in a Bose-Einstein condensate in a one-dimensional optical lattice. We find that quantum effects can be important and that it is even possible for the vortex to be strongly squeezed, which reflects itself in a different quantum mechanical uncertainty of the vortex position in two orthogonal directions. The latter is observable by measuring the atomic density after an expansion of the Bose-Einstein condensate in the lattice.Comment: 8 pages, 3 figures, more details added, some new citation

Hysteresis effects in rotating Bose-Einstein condensates

We study the formation of vortices in a dilute Bose-Einstein condensate confined in a rotating anisotropic trap. We find that the number of vortices and angular momentum attained by the condensate depends upon the rotation history of the trap and on the number of vortices present in the condensate initially. A simplified model based on hydrodynamic equations is developed, and used to explain this effect in terms of a shift in the resonance frequency of the quadrupole mode of the condensate in the presence of a vortex lattice. Differences between the spin-up and spin-down response of the condensate are found, demonstrating hysteresis phenomena in this system.Comment: 16 pages, 7 figures; revised after referees' report

Production Efficiency of Ultracold Feshbach Molecules in Bosonic and Fermionic Systems

We investigate the production efficiency of ultracold molecules in bosonic $^{85}$Rb and fermionic $^{40}$K when the magnetic field is swept across a Feshbach resonance. For adiabatic sweeps of the magnetic field, the conversion efficiency of each species is solely determined by the phase space density of the atomic cloud, in contrast to a number of theoretical predictions. Our novel model for the adiabatic pairing process, developed from general physical principles, accurately predicts the conversion efficiency for {\it both} ultracold gases of bosons and of fermions. In the non-adiabatic regime our measurements of the $^{85}$Rb molecule conversion efficiency follow a Landau Zener model, with a conversion efficiency that is characterized by the density divided by the time derivative of the magnetic field.Comment: 5 pages, 3 figure

Bragg Spectroscopy of Vortex Lattices in Bose-Einstein condensates

We have measured the velocity field of a vortex lattice within a sodium Bose-Einstein condensate using Bragg scattering. The phase gradient of the macroscopic wavefunction was mapped into the spatial structure of the diffracted atom cloud, allowing for single shot measurement of the rotation parameters. A combination of spectral and spatial information yields a complete description of the superfluid flow, coarse-grained over the lattice structure, including direct and independent measurements of the rate and sense of rotation. Signatures of the microscopic quantum rotation have also been observed.Comment: 5 pages, 5 Figures, A movie built from the CM data is available in our Webpage: http://www.physics.gatech.edu/chandra/index.htm; added Fig.5 presents new data, showing signatures of the microscopic vortex structure in the diffracted clou

The Experimental Observation of a Superfluid Gyroscope in a dilute Bose Condensed Gas

We have observed a superfluid gyroscope effect in a dilute gas Bose-Einstein condensate. A condensate with a vortex possesses a single quantum of angular momentum and this causes the plane of oscillation of the scissors mode to precess around the vortex line. We have measured the precession rate of the scissors oscillation. From this we deduced the angular momentum associated with the vortex line and found a value close to $\hbar$ per particle, as predicted for a superfluid.Comment: 4 pages 5 fig