Characterization of elastic scattering near a Feshbach resonance in rubidium 87

The s-wave scattering length for elastic collisions between 87Rb atoms in the state |f,m_f>=|1,1> is measured in the vicinity of a Feshbach resonance near 1007 G. Experimentally, the scattering length is determined from the mean-field driven expansion of a Bose-Einstein condensate in a homogeneous magnetic field. The scattering length is measured as a function of the magnetic field and agrees with the theoretical expectation. The position and the width of the resonance are determined to be 1007.40 G and 0.20 G, respectively.Comment: 4 pages, 2 figures minor revisions: added Ref.6, included error bar

Bose-Einstein condensate collapse: a comparison between theory and experiment

We solve the Gross-Pitaevskii equation numerically for the collapse induced by a switch from positive to negative scattering lengths. We compare our results with experiments performed at JILA with Bose-Einstein condensates of Rb-85, in which the scattering length was controlled using a Feshbach resonance. Building on previous theoretical work we identify quantitative differences between the predictions of mean-field theory and the results of the experiments. Besides the previously reported difference between the predicted and observed critical atom number for collapse, we also find that the predicted collapse times systematically exceed those observed experimentally. Quantum field effects, such as fragmentation, that might account for these discrepancies are discussed.Comment: 4 pages, 2 figure

Mean-field analysis of collapsing and exploding Bose-Einstein condensates

The dynamics of collapsing and exploding trapped Bose-Einstein condensat es caused by a sudden switch of interactions from repulsive to attractive a re studied by numerically integrating the Gross-Pitaevskii equation with atomic loss for an axially symmetric trap. We investigate the decay rate of condensates and the phenomena of bursts and jets of atoms, and compare our results with those of the experiments performed by E. A. Donley {\it et al.} [Nature {\bf 412}, 295 (2001)]. Our study suggests that the condensate decay and the burst production is due to local intermittent implosions in the condensate, and that atomic clouds of bursts and jets are coherent. We also predict nonlinear pattern formation caused by the density instability of attractive condensates.Comment: 7 pages, 8 figures, axi-symmetric results are adde

Critical number of atoms for attractive Bose-Einstein condensates with cylindrically symmetrical traps

We calculated, within the Gross-Pitaevskii formalism, the critical number of atoms for Bose-Einstein condensates with two-body attractive interactions in cylindrical traps with different frequency ratios. In particular, by using the trap geometries considered by the JILA group [Phys. Rev. Lett. 86, 4211 (2001)], we show that the theoretical maximum critical numbers are given approximately by $N_c = 0.55 ({l_0}/{|a|})$. Our results also show that, by exchanging the frequencies $\omega_z$ and $\omega_\rho$, the geometry with $\omega_\rho < \omega_z$ favors the condensation of larger number of particles. We also simulate the time evolution of the condensate when changing the ground state from $a=0$ to $a<0$ using a 200ms ramp. A conjecture on higher order nonlinear effects is also added in our analysis with an experimental proposal to determine its signal and strength.Comment: (4 pages, 2 figures) To appear in Physical Review

Mean-field description of collapsing and exploding Bose-Einstein condensates

We perform numerical simulation based on the time-dependent mean-field Gross-Pitaevskii equation to understand some aspects of a recent experiment by Donley et al. on the dynamics of collapsing and exploding Bose-Einstein condensates of $^{85}$Rb atoms. They manipulated the atomic interaction by an external magnetic field via a Feshbach resonance, thus changing the repulsive condensate into an attractive one and vice versa. In the actual experiment they changed suddenly the scattering length of atomic interaction from positive to a large negative value on a pre-formed condensate in an axially symmetric trap. Consequently, the condensate collapses and ejects atoms via explosion. We find that the present mean-field analysis can explain some aspects of the dynamics of the collapsing and exploding Bose-Einstein condensates.Comment: 9 Latex pages, 10 ps and eps files, version accepted in Physical Review A, minor changes mad

Saturation in heteronuclear photoassociation of 6Li7Li

We report heteronuclear photoassociation spectroscopy in a mixture of magneto-optically trapped 6Li and 7Li. Hyperfine resolved spectra of the vibrational level v=83 of the singlet state have been taken up to intensities of 1000 W/cm^2. Saturation of the photoassociation rate has been observed for two hyperfine transitions, which can be shown to be due to saturation of the rate coefficient near the unitarity limit. Saturation intensities on the order of 40 W/cm^2 can be determined.Comment: 5 pages, 3 figures, to appear in Phys. Rev. A (Rapid Communication

Model study on the photoassociation of a pair of trapped atoms into an ultralong-range molecule

Using the method of quantum-defect theory, we calculate the ultralong-range molecular vibrational states near the dissociation threshold of a diatomic molecular potential which asymptotically varies as $-1/R^3$. The properties of these states are of considerable interest as they can be formed by photoassociation (PA) of two ground state atoms. The Franck-Condon overlap integrals between the harmonically trapped atom-pair states and the ultralong-range molecular vibrational states are estimated and compared with their values for a pair of untrapped free atoms in the low-energy scattering state. We find that the binding between a pair of ground-state atoms by a harmonic trap has significant effect on the Franck-Condon integrals and thus can be used to influence PA. Trap-induced binding between two ground-state atoms may facilitate coherent PA dynamics between the two atoms and the photoassociated diatomic molecule.Comment: 11 pages, 4 figures, to appear in Phys. Rev. A (September, 2003

Stability of the trapped nonconservative Gross-Pitaevskii equation with attractive two-body interaction

The dynamics of a nonconservative Gross-Pitaevskii equation for trapped atomic systems with attractive two-body interaction is numerically investigated, considering wide variations of the nonconservative parameters, related to atomic feeding and dissipation. We study the possible limitations of the mean field description for an atomic condensate with attractive two-body interaction, by defining the parameter regions where stable or unstable formation can be found. The present study is useful and timely considering the possibility of large variations of attractive two-body scattering lengths, which may be feasible in recent experiments.Comment: 6 pages, 5 figures, submitted to Physical Review

Three-body non-additive forces between spin-polarized alkali atoms

Three-body non-additive forces in systems of three spin-polarized alkali atoms (Li, Na, K, Rb and Cs) are investigated using high-level ab initio calculations. The non-additive forces are found to be large, especially near the equilateral equilibrium geometries. For Li, they increase the three-atom potential well depth by a factor of 4 and reduce the equilibrium interatomic distance by 0.9 A. The non-additive forces originate principally from chemical bonding arising from sp mixing effects.Comment: 4 pages, 3 figures (in 5 files

Ground state and elementary excitations of single and binary Bose-Einstein condensates of trapped dipolar gases

We analyze the ground-state properties and the excitation spectrum of Bose-Einstein condensates of trapped dipolar particles. First, we consider the case of a single-component polarized dipolar gas. For this case we discuss the influence of the trapping geometry on the stability of the condensate as well as the effects of the dipole-dipole interaction on the excitation spectrum. We discuss also the ground state and excitations of a gas composed of two antiparallel dipolar components.Comment: 12 pages, 9 eps figures, final versio