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arXiv:cond-mat/9903414 · Physical Review A

Atom loss from Bose-Einstein condensates due to Feshbach resonance

Vladimir Yurovsky, A. Ben‐Reuven, Paul S. Julienne, Carl J. Williams

Published Aug 1, 1999• 84 citations
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Abstract

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 $\ensuremath{\sim}{10}^{\ensuremath{-}10} {\mathrm{cm}}^{3}/\mathrm{s}.$

DOI
10.1103/physreva.60.r765

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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∼10\ensuremath−10cm3/s.\ensuremath{\sim}{10}^{\ensuremath{-}10} {\mathrm{cm}}^{3}/\mathrm{s}.\ensuremath∼10\ensuremath−10cm3/s.
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.
We study Feshbach resonance scattering in a time-dependent magnetic field. We explain the extremely rapid decay observed in a recent experiment investigating Feshbach resonances in a Na Bose-Einstein condensate. In our picture, the decay is stimulated by the formation of a molecular condensate of quasibound atom pairs. Another essential element is the concept of a global and a local resonance lifetime. The predicted decay rates are large, about 5 orders of magnitude larger than typical dipole decay rates, and 1 order larger than typical exchange decay rates. We point out the possible role of a Josephson-like oscillation between the atomic condensate and a long-range molecular condensate.
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.
Recently, effects of Feshbach resonances in atom-atom interactions were observed by varying the external magnetic field of an atomic Bose-Einstein condensate (BEC). We point out that the quasi-bound molecules created in the intermediate state of the resonance can form a second, molecular condensate. The many-body state of the system is then a hybrid atomic/molecular condensate with inter-condensate tunneling of atom pairs. A sudden variation of the magnetic field results in oscillations of the number of atoms and molecules in their respective condensates, providing a signature of this novel type of quantum tunneling.
Recent Feshbach-resonance experiments with 85Rb Bose-Einstein condensates have led to a host of unexplained results: dramatic losses of condensate atoms for an across-resonance sweep of the magnetic field, a collapsing condensate with a burst of atoms emanating from the remnant condensate, increased losses for decreasing interaction times--until very short times are reached, and coherent oscillations between remnant and burst atoms. In particular, the amplitude of the remnant-burst oscillations, and the corresponding missing atoms, have prompted speculation as to the formation of a molecular condensate. Using a minimal mean-field model, we find that rogue dissociation, molecular dissociation to noncondensate atom pairs, is qualitatively implicated as the physical mechanism responsible for these observations, although very little molecular condensate is formed. Refining the model provides excellent quantitative agreement with the experimental remnant-burst oscillations, and the fraction of molecular condensate accounts almost entirely for the measured atom loss.
Recent Feshbach-resonance experiments with 85Rb Bose-Einstein condensates have led to a host of unexplained results: dramatic losses of condensate atoms for an across-resonance sweep of the magnetic field, a collapsing condensate with a burst of atoms emanating from the remnant condensate, increased losses for decreasing interaction times, and coherent oscillations between remnant and burst atoms. Using a simple yet realistic mean-field model, we find that rogue dissociation, molecular dissociation to noncondensate atom pairs, is strongly implicated as the physical mechanism responsible for these observations.