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arXiv:cond-mat/0204504 · Physical Review Letters

Ramsey Fringes in a Bose-Einstein Condensate between Atoms and Molecules

S. J. J. M. F. Kokkelmans, Murray Holland

Published Oct 11, 2002• 147 citations
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Abstract

In a recent experiment, a Feshbach scattering resonance was exploited to observe Ramsey fringes in a 85Rb Bose-Einstein condensate. The oscillation frequency corresponded to the binding energy of the molecular state. We show that the observations are remarkably consistent with predictions of a resonance field theory in which the fringes arise from oscillations between atoms and molecules.

DOI
10.1103/physrevlett.89.180401

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In a recent experiment, a Feshbach scattering resonance was exploited to observe Ramsey fringes in a 85Rb Bose-Einstein condensate. The oscillation frequency corresponded to the binding energy of the molecular state. We show that the observations are remarkably consistent with predictions of a resonance field theory in which the fringes arise from oscillations between atoms and molecules.
We discuss the frequency and visibility of atom-molecule Ramsey fringes observed in recent experiments by Claussen et al. [Phys. Rev. A 67, 060701 (2003)]. In these experiments a 85Rb^{85}\mathrm{Rb}85Rb Bose-Einstein condensate was exposed to a sequence of magnetic field pulses on the high-field side of the 155G155\phantom{\rule{0.3em}{0ex}}\mathrm{G}155G Feshbach resonance. The observed oscillation frequencies largely agree with the theoretically predicted magnetic field dependence of the binding energy of the highest excited diatomic vibrational state, except for a small region very close to the singularity of the scattering length. Our analytic treatment of the experiment, as well as our dynamical simulations, follow the magnitude of the measured oscillation frequencies as well as the visibilities of the Ramsey fringes. We show that significant deviations from a purely binary dynamics, with an associated binding frequency, occur when the spatial extent of the molecular wave function becomes comparable with the mean distance between the atoms in the dilute gas. The experiments thus clearly identify the conditions under which diatomic molecules may be identified as a separate entity of the gas or, conversely, when the concept of binary physics in a many-body environment is bound to break down.
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.
In Phys. Rev. Lett. 89, 180401 (2002) [cond-mat/0204504], Kokkelmans and Holland interpret the results of a recent experiment at JILA that demonstrated atom-molecule coherence in a Bose-Einstein condensate. Using a mean-field approximation to a resonance field theory involving an atom condensate and a molecular condensate, they find that the molecular condensate is tiny compared to the atom condensate. We show that if the probability for the molecular field to create a diatomic molecule is correctly included, the numbers of atoms in the atom condensate and in the condensate of diatomic molecules are comparable.
We create atom-molecule superpositions in a Bose-Fermi mixture of 87Rb^{87}\text{R}\text{b}87Rb and 40K^{40}\text{K}40K atoms. The superpositions are generated by ramping an applied magnetic field near an interspecies Fano-Feshbach resonance to coherently couple atom and molecule states. Rabi- and Ramsey-type experiments show oscillations in the molecule population that persist as long as $150\text{ }\ensuremath{\mu}\text{s}$ and have up to 50% contrast. The frequencies of these oscillations are magnetic-field dependent and consistent with the predicted molecule binding energy. This quantum superposition involves a molecule and a pair of free particles with different statistics (i.e., bosons and fermions) and furthers exploration of atom-molecule coherence in systems without a Bose-Einstein condensate.
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
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 ${\ensuremath{\epsilon}}_{\mathrm{bind}}.$