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arXiv:cond-mat/0302195 · Physical Review A

Very-high-precision bound-state spectroscopy near a 85Rb Feshbach resonance

N. R. Claussen, S. J. J. M. F. Kokkelmans, S. T. Thompson, Elizabeth A. Donley, E. Hodby, Carl Wieman

Published Jun 20, 2003• 146 citations
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Abstract

We precisely measured the binding energy $({\ensuremath{\epsilon}}_{\mathrm{bind}})$ of a molecular state near the Feshbach resonance in a ${}^{85}\mathrm{Rb}$ 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 ${\ensuremath{\epsilon}}_{\mathrm{bind}}.$

DOI
10.1103/physreva.67.060701

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WORLD SCIENTIFIC eBooks•Jan 1, 2008•1 citation
We precisely measured the binding energy (\ensuremathϵbind)({\ensuremath{\epsilon}}_{\mathrm{bind}})(\ensuremathϵbind​) 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)a0][\ensuremath{-}{443(3)a}_{0}][\ensuremath−443(3)a0​] 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 \ensuremathϵbind.{\ensuremath{\epsilon}}_{\mathrm{bind}}.\ensuremathϵbind​.
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.
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
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.
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.
Bose-Einstein condensation (BEC) of Feshbach molecules in a homogeneous Bose gas is studied at finite temperatures in a single-channel mean-field approach where the Hartree-Fock energy and pairing gap are determined self-consistently. In the molecular-BEC state, the atomic excitation is gapped and the molecular excitation is gapless. The binding energy of Feshbach molecules is shifted from the vacuum value by many-body effects. When the scattering length as{a}_{s}as​ of the atoms is negative, the system is subject to mechanical collapse due to negative compressibility. The system is stable in most regions with positive scattering lengths. However, at low temperatures near the resonance, the molecular-BEC state vanishes, and the coherent mixture of atomic and molecular BEC is subject to mechanical collapse.
Abstract Recent advances in the precise control of ultracold atomic systems have led to the realisation of Bose–Einstein condensates (BECs) and degenerate Fermi gases. An important challenge is to extend this level of control to more complicated molecular systems. One route for producing ultracold molecules is to form them from the atoms in a BEC. For example, a two-photon stimulated Raman transition in a 87Rb BEC has been used to produce 87Rb2 molecules in a single rotational-vibrational state1, and ultracold molecules have also been formed2 through photoassociation of a sodium BEC. Although the coherence properties of such systems have not hitherto been probed, the prospect of creating a superposition of atomic and molecular condensates has initiated much theoretical work3, 4, 5, 6, 7. Here we make use of a time-varying magnetic field near a Feshbach resonance8, 9, 10, 11, 12 to produce coherent coupling between atoms and molecules in a 85Rb BEC. A mixture of atomic and molecular states is created and probed by sudden changes in the magnetic field, which lead to oscillations in the number of atoms that remain in the condensate. The oscillation frequency, measured over a large range of magnetic fields, is in excellent agreement with the theoretical molecular binding energy, indicating that we have created a quantum superposition of atoms and diatomic molecules—two chemically different species.