Dynamic depletion in a Bose condensate via a sudden increase of the scattering length

We examine the time-dependent quantum depletion of a trapped Bose condensate arising from a rapid increase of the scattering length. Our solution indicates that a significant buildup of incoherent atoms can occur within a characteristic time short compared with the harmonic trap period. We discuss how the depletion density and the characteristic time depend on the physical parameters of the condensate

Report on Experiment E349: Quasifree Radiative Capture in the Deuteron

This research was sponsored by the National Science Foundation Grant NSF PHY-931478

Very high precision bound state spectroscopy near a 85^{85}Rb Feshbach resonance

We precisely measured the binding energy of a molecular state near the Feshbach resonance in a $^{85}$Rb Bose-Einstein condensate (BEC). Rapid magnetic field pulses induced coherent atom-molecule oscillations in the BEC. We measured the oscillation frequency as a function of B-field and fit the data to a coupled-channels model. Our analysis constrained the Feshbach resonance position [155.041(18) G], width [10.71(2) G], and background scattering length [-443(3) a$_0$] and yielded new values for $v_{DS}$, $v_{DT}$, and $C_6$. These results improved our estimate for the stability condition of an attractive BEC. We also found evidence for a mean-field shift to the binding energy.Comment: 5 pages, 2 figures, submitted to PR

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

Properties of a Dilute Bose Gas near a Feshbach Resonance

In this paper, properties of a homogeneous Bose gas with a Feshbach resonance are studied in the dilute region at zero temperature. The stationary state contains condensations of atoms and molecules. The ratio of the molecule density to the atom density is $\pi na^3$. There are two types of excitations, molecular excitations and atomic excitations. Atomic excitations are gapless, consistent with the traditional theory of a dilute Bose gas. The molecular excitation energy is finite in the long wavelength limit as observed in recent experiments on $^{85}$Rb. In addition, the decay process of the condensate is studied. The coefficient of the three-body recombination rate is about 140 times larger than that of a Bose gas without a Feshbach resonance, in reasonably good agreement with the experiment on $^{23}$Na.Comment: 11 pages, 1 figure, comparison between the calculated three-body recombination rate and the experimental data for Na system has been adde

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

Weakly bound atomic trimers in ultracold traps

The experimental three-atom recombination coefficients of the atomic states $^{23}$Na$|F=1,m_F=-1>$, $^{87}$Rb$|F=1,m_F=-1>$ and $^{85}$Rb$|F=2,m_F=-2>$, together with the corresponding two-body scattering lengths, allow predictions of the trimer bound state energies for such systems in a trap. The recombination parameter is given as a function of the weakly bound trimer energies, which are in the interval $1<m(a/\hbar)^2 E_3< 6.9$ for large positive scattering lengths, $a$. The contribution of a deep-bound state to our prediction, in the case of $^{85}$Rb$|F=2,m_F=-2>$, for a particular trap, is shown to be relatively small.Comment: 5 pages, 1 figur

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

Scaling predictions for radii of weakly bound triatomic molecules

The mean-square radii of the molecules $^4$He$_3$, $^4$He$_2-^6$Li, $^4$He$_2-^7$Li and $^4$He$_2-^{23}$Na are calculated using a three-body model with contact interactions. They are obtained from a universal scaling function calculated within a renormalized scheme for three particles interacting through pairwise Dirac-delta interaction. The root-mean-square distance between two atoms of mass $m_A$ in a triatomic molecule are estimated to be of de order of ${\cal C}\sqrt{\hbar^2/[m_A(E_3-E_2)]}$, where $E_2$ is the dimer and $E_3$ the trimer binding energies, and ${\cal C}$ is a constant (varying from $\sim 0.6$ to $\sim 1$) that depends on the ratio between $E_2$ and $E_3$. Considering previous estimates for the trimer energies, we also predict the sizes of Rubidium and Sodium trimers in atomic traps.Comment: 7 pages, 2 figure