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arXiv:cond-mat/0211514 · Physical Review A

Dynamics of a Bose-Einstein condensate near a Feshbach resonance

R. A. Duine, Henk T. C. Stoof

Published Jul 9, 2003• 41 citations
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Abstract

We discuss the response of a Bose-Einstein condensate to a change in the scattering length, which is experimentally realized by tuning the magnetic field near a Feshbach resonance. In particular, we consider the collapse of the condensate induced by a sudden change in the scattering length from a large positive to a small negative value. We also consider the condensate dynamics that results from a single pulse in the magnetic field, due to which the scattering length is rapidly increased from zero to a large value and then after some time rapidly decreased again to its initial value. We focus primarily on the consequences of the quantum evaporation process on the dynamics of the Bose-Einstein condensate, but also discuss the effects of atom-molecule coherence.

DOI
10.1103/physreva.68.013602

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We discuss the response of a Bose-Einstein condensate to a change in the scattering length, which is experimentally realized by tuning the magnetic field near a Feshbach resonance. In particular, we consider the collapse of the condensate induced by a sudden change in the scattering length from a large positive to a small negative value. We also consider the condensate dynamics that results from a single pulse in the magnetic field, due to which the scattering length is rapidly increased from zero to a large value and then after some time rapidly decreased again to its initial value. We focus primarily on the consequences of the quantum evaporation process on the dynamics of the Bose-Einstein condensate, but also discuss the effects of atom-molecule coherence.
The achievement of a Bose-Einstein condensate of cesium in the lowest internal state (F=3, m/sub F/=3) by evaporative cooling in an optical trap is reported. The corresponding scattering length shows a strong dependence on magnetic field, varying from large negative to large positive values in a conveniently accessible magnetic field range due to a unusual combination of broad and narrow Feshbach resonances. The inelastic processes resulting from this complex scattering behavior in thermal ensembles is studied. These measurements have been of crucial importance for identifying a suitable path in phase space towards condensation. In first experiments, the strong dependence of the condensate mean-field energy on the magnetic field is demonstrated. By briefly switching to different scattering lengths just before releasing the sample from the trap, imploding, exploding, and non-interacting 'frozen' condensates are produced. We will employ the tunable interaction in further experiments by looking at molecule formation on Feshbach resonances and exploring condensate dynamics at extreme values of the scattering length.
We show that a Bose-Einstein condensate emits atoms, if either the condensate wave function, or the scattering length of the atoms depends strongly on time. Moreover, the emission process is coherent and atoms can oscillate back and forth between the condensate and the excited states. Inspired by recent experimental results, we present results of simulations of the response of a Bose-Einstein condensate to a very rapid change in the scattering length. The possibility of molecule formation is also discussed.
Bose-Einstein condensation has been achieved in a magnetically trapped sample of 85Rb atoms. Stable condensates of up to 104 atoms have been created by using a magnetic-field-induced Feshbach resonance to reverse the sign of the zero-field scattering length. These condensates provide unique opportunities for the study of BEC physics. The variation of the scattering length near the resonance has been used to magnetically tune the condensate self-interaction energy over a very wide range. This range extended from very strong repulsive self-interactions to large attractive ones. The effect of moving the condensate through the Feshbach resonance has been studied and compared with theory. Long-lived metastable condensates with attractive interactions have been produced near the zero of the Feshbach resonance. The transition from repulsive to attractive interactions can lead to a “collapse” of the condensate in which the cloud shrinks below our resolution limit, loses a significant number of atoms due to inelastic losses, and emits a burst of high-energy atoms.
Atom–molecule coherence in a Bose-Einstein condensate (BEC) has been demonstrated. Sudden changes were made to the magnetic field near a Feshbach resonance such that oscillations between atomic and molecular states were excited. The frequency of these oscillations was measured over a large range of magnetic fields and was found to be in excellent quantitative agreement with the predicted energy difference between two colliding atoms and the bound molecular state. This agreement indicates that we have created a quantum superposition of atoms and diatomic molecules, which are chemically different species. 1
The properties of Bose-Einstein condensed gases can be strongly altered by tuning the external magnetic field near a Feshbach resonance. Feshbach resonances affect elastic collisions and lead to the observed modification of the scattering length. However, as we report here, the observed rate of inelastic collisions was strongly enhanced in a sodium Bose-Einstein condensate when the scattering length was tuned to both larger or smaller values than the off-resonant value. These strong losses impose severe limitations for using Feshbach resonances to tune the properties of Bose-Einstein condensates.
We rapidly change the scattering length as{a}_{s}as​ of a 87{}^{87}87Rb Bose-Einstein condensate by means of a Feshbach resonance, simultaneously releasing the condensate from its harmonic trapping potential. When as{a}_{s}as​ is changed from positive to negative, the subsequent collapse of the condensate is stabilized by the kinetic energy imparted during the release, resulting in a deceleration of the loss rate near the resonance. We also observe an increase in the Thomas-Fermi radius, near the resonance, that cannot be understood in terms of a simple scaling model. Instead, we describe this behavior using the Gross-Pitaevskii equation, including three-body recombination, and hypothesize that the increase in cloud radius is due to self-interference of the condensate resulting in the formation of concentric shells.