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

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

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

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

Autler-Townes splitting in two-color photoassociation of 6Li

We report on high-resolution two-color photoassociation spectroscopy in the triplet system of magneto-optically trapped 6Li. The absolute transition frequencies have been measured. Strong optical coupling of the bound molecular states has been observed as Autler-Townes splitting in the photoassociation signal. The spontaneous bound-bound transition rate is determined and the molecule formation rate is estimated. The observed lineshapes are in good agreement with the theoretical model.Comment: 5 pages, 4 figures, accepted for publication in Phys. Rev. A (Rapid Communication

Control of an atom laser using feedback

A generalised method of using feedback to control Bose-Einstein condensates is introduced. The condensates are modelled by the Gross-Pitaevskii equation, so only semiclassical fluctations can be suppressed, and back-action from the measurement is ignored. We show that for any available control, a feedback scheme can be found to reduce the energy while the appropriate moment is still dynamic. We demonstrate these schemes by considering a condensate trapped in a harmonic potential that can be modulated in strength and position. The formalism of our feedback scheme also allows the inclusion of certain types of non-linear controls. If the non-linear interaction between the atoms can be controlled via a Feshbach resonance, we show that the feedback process can operate with a much higher efficiency.Comment: 6 pages, 7 figure

Collapse dynamics of trapped Bose-Einstein condensates

We analyze the implosion and subsequent explosion of a trapped condensate after the scattering length is switched to a negative value. Our results compare very well qualitatively and fairly well quantitatively with the results of recent experiments at JILA.Comment: 4 pages, 3 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

Effect of anharmonicities in the critical number of trapped condensed atoms with attractive two-body interaction

We determine the quantitative effect, in the maximum number of particles and other static observables, due to small anharmonic terms added to the confining potential of an atomic condensed system with negative two-body interaction. As an example of how a cubic or quartic anharmonic term can affect the maximum number of particles, we consider the trap parameters and the results given by Roberts et al. [Phys. Rev. Lett. 86, 4211 (2001)]. However, this study can be easily transferred to other trap geometries to estimate anharmonic effects.Comment: Total of 5 pages, 3 figures and 1 table. To appear in Phys. Rev.

Modulated Amplitude Waves in Bose-Einstein Condensates

We analyze spatio-temporal structures in the Gross-Pitaevskii equation to study the dynamics of quasi-one-dimensional Bose-Einstein condensates (BECs) with mean-field interactions. A coherent structure ansatz yields a parametrically forced nonlinear oscillator, to which we apply Lindstedt's method and multiple-scale perturbation theory to determine the dependence of the intensity of periodic orbits (``modulated amplitude waves'') on their wave number. We explore BEC band structure in detail using Hamiltonian perturbation theory and supporting numerical simulations.Comment: 5 pages, 4 figs, revtex, final form of paper, to appear in PRE (forgot to include \bibliography command in last update, so this is a correction of that; the bibliography is hence present again