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arXiv:cond-mat/0505180 · Physical Review A

Formation of molecules from a Cs Bose-Einstein condensate

Vladimir Yurovsky, A. Ben‐Reuven

Published Nov 17, 2005• 12 citations
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Abstract

Conversion of an expanding Bose-Einstein condensate of Cs atoms to a molecular one with an efficiency of more than 30% was observed recently in experiments by M. Mark et al. [Europhys. Lett. 69, 706 (2005)]. The theory presented here describes the experimental results. Values of resonance strength of 8 mG and rate coefficients for atom-molecule deactivation of $1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}11}\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{3}∕\mathrm{s}$ and molecule-molecule one of $1.5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}9}\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{3}∕\mathrm{s}$ are estimated by a fit of the theoretical results to the experimental data. Near the resonance, where the highest conversion efficiency was observed, the results demonstrate strong sensitivity to the magnetic field ripple and inhomogeneity. A conversion efficiency of about 60% is predicted by non-mean-field calculations for densities and sweep rates lower than the ones used in the experiments.

DOI
10.1103/physreva.72.053618

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Conversion of an expanding Bose-Einstein condensate of Cs atoms to a molecular one with an efficiency of more than 30% was observed recently in experiments by M. Mark et al. [Europhys. Lett. 69, 706 (2005)]. The theory presented here describes the experimental results. Values of resonance strength of 8 mG and rate coefficients for atom-molecule deactivation of 1\ifmmode×\else\texttimes\fi10\ensuremath−11cm3∕s1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}11}\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{3}∕\mathrm{s}1\ifmmode×\else\texttimes\fi10\ensuremath−11cm3∕s and molecule-molecule one of 1.5\ifmmode×\else\texttimes\fi10\ensuremath−9cm3∕s1.5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}9}\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{3}∕\mathrm{s}1.5\ifmmode×\else\texttimes\fi10\ensuremath−9cm3∕s are estimated by a fit of the theoretical results to the experimental data. Near the resonance, where the highest conversion efficiency was observed, the results demonstrate strong sensitivity to the magnetic field ripple and inhomogeneity. A conversion efficiency of about 60% is predicted by non-mean-field calculations for densities and sweep rates lower than the ones used in the experiments.
In experiments conducted recently at MIT on Na Bose-Einstein condensates [S. Inouye et al., Nature (London) 392, 151 (1998); J. Stenger et al., Phys. Rev. Lett. 82, 2422 (1999)], large loss rates were observed when a time-varying magnetic field was used to tune a molecular Feshbach resonance state near the state of a pair of atoms in the condensate. A collisional deactivation mechanism affecting a temporarily formed molecular condensate [see V. A. Yurovsky, A. Ben-Reuven, P. S. Julienne and C. J. Williams, Phys. Rev. A 60, R765 (1999)], studied here in more detail, accounts for the results of the slow-sweep experiments. A best fit to the MIT data yields a rate coefficient for deactivating atom-molecule collisions of $1.6\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10} {\mathrm{cm}}^{3}/\mathrm{s}.$ In the case of the fast-sweep experiment, a study is carried out of the combined effect of two competing mechanisms, the three-atom (atom-molecule) or four-atom (molecule-molecule) collisional deactivation versus a process of two-atom trap-state excitation by curve crossing [F. H. Mies, P. S. Julienne, and E. Tiesinga, Phys. Rev. A 61, 022721 (2000)]. It is shown that both mechanisms contribute to the loss comparably and nonadditively.
In recent experiments on Na Bose-Einstein condensates [S. Inouye et al., Nature 392, 151 (1998); J. Stenger et al., Phys. Rev. Lett. 82, 2422 (1999)], large loss rates were observed when a time-varying magnetic field was used to tune a molecular Feshbach resonance state near the state of atom pairs that belong to the condensate many-body wave function. A mechanism is offered here to account for the observed losses. It is based on the deactivation of the resonant molecular state by interaction with a third condensate atom, with a deactivation rate coefficient of magnitude $\ensuremath{\sim}{10}^{\ensuremath{-}10} {\mathrm{cm}}^{3}/\mathrm{s}.$
A theoretical analysis of expanding hybrid atom-molecule Bose-Einstein condensates is presented with application to the recent experiments of the Rempe group on 87Rb^{87}\mathrm{Rb}87Rb, in which the formation of ultracold molecules by Feshbach resonance was demonstrated. A mean-field approach is used to describe the molecular association process. The subsequent dissociation of the molecules is treated using a non-mean-field parametric approximation. The latter method is also used to derive optimal conditions for the formation of a molecular condensate.
We report a new scheme to create weakly bound Cs 2 molecules from an atomic Bose-Einstein condensate. The method is based on switching the magnetic field to a narrow Feshbach resonance and yields a high atom-molecule conversion efficiency of more than 30%, a factor of three higher than obtained with conventional magnetic-field ramps. The Cs 2 molecules are created in a single g -wave rotational quantum state. The observed dependence of the conversion efficiency on the magnetic field and atom density shows scattering processes beyond two-body coupling to occur in the vicinity of the Feshbach resonance.
We present a theoretical model for Bragg scattering from a Bose-Einstein condensate (BEC) in the vicinity of a magnetic Feshbach resonance, using a two c-field formalism, one c-field for the atom and the other for a molecule formed of two atoms. We use this model to numerically simulate a recent experiment [S. B. Papp et al., Phys. Rev. Lett., 101(13):135301, Sep 2008] investigating the effects of strong interactions on the Bragg spectrum from a 85Rb BEC. Results from these simulations are in very good quantitative agreement with the experimental results, confirming the importance of the resonance bound state in the dynamics of the condensate for fast experiments like Bragg scattering.
Ultracold sodium molecules were produced from an atomic Bose-Einstein condensate by ramping an applied magnetic field across a Feshbach resonance. More than 10(5) molecules were generated with a conversion efficiency of approximately 4%. Using laser light resonant with an atomic transition, the remaining atoms could be selectively removed, preventing fast collisional relaxation of the molecules. Time-of-flight analysis of the pure molecular sample yielded an instantaneous phase-space density greater than 20.