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arXiv:cond-mat/0306218

Coherent dimer formation near Feshbach resonances in Bose-Einstein condensates

Victo S. Filho, Lauro Tomio, A. Gammal, T. Frederico

Published Jun 9, 2003• 0 citations
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Abstract

The results of a recent experiment with $^{85}$Rb Bose-Einstein condensates are analyzed within the mean-field approximation including dissipation due to three-body recombination. The intensity of the dissipative term is chosen from the three-body theory for large positive scattering lengths. The remaining number of condensed atoms in the experiment, obtained with applied magnetic field pulses, were used to adjust the intensity of the dissipative term. We found that the three-body recombination parameter depends on the pulse rise time; i.e., for longer rise times the values found become consistent with the three-body theory, while for shorter pulses this coefficient is found to be much larger. We interpret this finding as an indication of a coherent formation of dimers.

DOI
10.48550/arxiv.cond-mat/0306218

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WORLD SCIENTIFIC eBooks•Jan 1, 2008•1 citation
The results of a recent experiment with 85^{85}85Rb Bose-Einstein condensates are analyzed within the mean-field approximation including dissipation due to three-body recombination. The intensity of the dissipative term is chosen from the three-body theory for large positive scattering lengths. The remaining number of condensed atoms in the experiment, obtained with applied magnetic field pulses, were used to adjust the intensity of the dissipative term. We found that the three-body recombination parameter depends on the pulse rise time; i.e., for longer rise times the values found become consistent with the three-body theory, while for shorter pulses this coefficient is found to be much larger. We interpret this finding as an indication of a coherent formation of dimers.
We predict the resonance-enhanced magnetic field dependence of atom-dimer relaxation and three-body recombination rates in a 87Rb^{87}\mathrm{Rb}87Rb Bose-Einstein condensate close to 1007G1007\phantom{\rule{0.3em}{0ex}}\mathrm{G}1007G. Our exact treatments of three-particle scattering explicitly include the dependence of the interactions on the atomic Zeeman levels. The Feshbach resonance distorts the entire diatomic energy spectrum, causing interferences in both loss phenomena. Our two independent experiments confirm the predicted recombination loss over a range of rate constants that spans four orders of magnitude.
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.
Atom loss resonances in ultracold trapped atoms have been observed at scattering lengths near atom-dimer resonances, at which Efimov trimers cross the atom-dimer threshold, and near two-dimer resonances, at which universal tetramers cross the dimer-dimer threshold. We propose a new mechanism for these loss resonances in a Bose-Einstein condensate of atoms. As the scattering length is ramped to the large final value at which the atom loss rate is measured, the time-dependent scattering length generates a small condensate of shallow dimers coherently from the atom condensate. The coexisting atom and dimer condensates can be described by a low-energy effective field theory with universal coefficients that are determined by matching exact results from few-body physics. The classical field equations for the atom and dimer condensates predict narrow enhancements in the atom loss rate near atom-dimer resonances and near two-dimer resonances due to inelastic dimer collisions.
We precisely measured the binding energy $({\ensuremath{\epsilon}}_{\mathrm{bind}})$ of a molecular state near the Feshbach resonance in a 85Rb{}^{85}\mathrm{Rb}85Rb Bose-Einstein condensate (BEC). Rapid magnetic-field pulses induced coherent atom-molecule oscillations in the BEC. We measured the oscillation frequency as a function of B field and fit the data to a coupled-channel model. Our analysis constrained the Feshbach resonance position [155.041(18) G], width [10.71(2) G], and background scattering length $[\ensuremath{-}{443(3)a}_{0}]$ and yielded new values for the Rb interaction parameters. These results improved our estimate for the stability condition of an attractive BEC. We also found evidence for a mean-field shift to ${\ensuremath{\epsilon}}_{\mathrm{bind}}.$
With help of a Feshbach scattering resonance it is possible to change the effective two-body interaction of ultra-cold atoms from repulsive to attractive, from weak to strong. Regular field theory for the description of Bose-Einstein condensates is based on a single interaction parameter only, the scattering length. Such a description, however, is not valid anymore for the resonance regime. We formulated a field-theory that incorporated the microscopic energy-dependent two-body interactions, that also takes pair correlations into account. This theory allowed us to explain an experiment at JILA where Ramsey fringes were observed in a ^85Rb Bose-Einstein condensate by making use of a Feshbach resonance. The theory and experiment show that coherent molecules are created, a first step in the direction of molecular BEC. For non-resonant interactions, the self-energy corresponding to the atom-atom interactions is proportional to the scattering length. Close to resonance, however, this relationship no longer applies, and the energy will level off to a finite value on resonance. We investigate this resonance self-energy, and compare it with experimental results from strongly interacting Fermi systems.
We precisely measured the binding energy ɛbind) of a molecular stale near the Feshbach resonance In a 85Rb Bose-Einstein condensate (BEC). Rapid magnetic-field pulses induced coherent atom-molecule oscillations in the BEC. We measured the oscillation frequency as a function B tield and fit the data TO a coupled-channel model. Our analysis constrained the Feshbach resonance position [155.041(18) Gl, width 10.71(2; G] and background scattering length [-443[3]a0] and yielded new values fur the Rb interaction parameters. These results improved our estimate lor the stability condition of an attractive BEC. We also found evidence for a mean-field shift to ɛbind.