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arXiv:cond-mat/0205267 · Physical Review A

Formation of a molecular Bose-Einstein condensate and an entangled atomic gas by Feshbach resonance

Vladimir Yurovsky, A. Ben‐Reuven

Published Apr 23, 2003• 50 citations
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Abstract

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.

DOI
10.1103/physreva.67.043611

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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.
Bose-Einstein condensate (BEC) is considered under conditions of Feshbach resonance in two-atom collisions due to a coupling of atomic pair and resonant molecular states. The association of condensate atoms can form a molecular BEC, and the molecules can dissociate to pairs of entangled atoms in two-mode squeezed states. Both entanglement and squeezing can be applied to quantum measurements and information processing. The processes in the atom-molecule quantum gas are analyzed using two theoretical approaches. The mean-field one takes into account deactivating collisions of resonant molecules with other atoms and molecules, neglecting quantum fluctuations. This method allows analysis of inhomogeneous systems, such as expanding BEC. The non-mean-field approach -- the parametric approximation -- takes into account both deactivation and quantum fluctuations. This method allows determination of optimal conditions for formation of molecular BEC and describes Bose-enhanced dissociation of molecular BEC, as well as entanglement and squeezing of the non-condensate atoms.
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.
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 consider the dissociation of a molecular Bose-Einstein condensate due to a magnetic-field sweep that starts on the molecular side of a Feshbach resonance and ends either on the atomic or on the molecular side. We determine both the time-dependent response of the molecular condensate wave function and the energy distribution of the atoms produced after the sweep. In the cases where experiments have been performed, our analytic and numerical calculations provide good agreement with experimental atomic energy distributions.
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.