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Physical Review Letters

Time-Dependent Feshbach Resonance Scattering and Anomalous Decay of a Na Bose-Einstein Condensate

Frank A. van Abeelen, BOUDEWIJN J. VERHAAR

Published Aug 23, 1999• 144 citations
Publisher

Abstract

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.

DOI
10.1103/physrevlett.83.1550

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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.
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 $\ensuremath{\sim}{10}^{\ensuremath{-}10} {\mathrm{cm}}^{3}/\mathrm{s}.$
Association in an atomic Bose-Einstein condensate, and dissociation of the resulting molecular condensate, due to a Feshbach resonance in a time-dependent magnetic field, are analyzed incorporating non-mean-field quantum corrections and inelastic collisions. Calculations for the Na atomic condensate demonstrate that there exist optimal conditions under which about 80% of the atomic population can be converted to a relatively long-lived molecular condensate (with lifetimes of 100 ms and more). Entangled atoms in two-mode squeezed states (with noise reduction of about 30 dB) may also be formed by molecular dissociation.
Association in an atomic Bose‐Einstein condensate, and the subsequent dissociation of the resulting molecular condensate, due to Feshbach resonance in a time‐dependent magnetic field, are analyzed, incorporating non‐mean‐field quantum corrections and inelastic collisions. Calculations for the Na atomic condensate demonstrate that there exist optimal conditions under which about 80% of the atomic population can be converted to a relatively long‐lived molecular condensate (with lifetimes of 10 ms and longer), if the magnetic field is temporally changed one way. Entangled atoms in two‐mode squeezed states (with noise reduction of about 30 dB) are formed by molecular dissociation when the field is changed the other way.
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 explore the zero-temperature statics of an atomic Bose-Einstein condensate in which a Feshbach resonance creates a coupling to a second condensate component of quasibound molecules. Using a variational procedure to find the equation of state, the appearance of this binding is manifest in a collapsing ground state, where only the molecular condensate is present up to some critical density. Further, an excited state is seen to reproduce the usual low-density atomic condensate behavior in this system, but the molecular component is found to produce a coherent, many-body decay, quantified by the imaginary part of the chemical potential. Most importantly, the unique decay rate dependencies on density (approximately rho (3/2)) and on scattering length (approximately (5/2)) can be measured in experimental tests of this result.
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.