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arXiv:0810.1965 · Physical Review A

Coherent atom-molecule oscillations in a Bose-Fermi mixture

M. L. Olsen, John D. Perreault, Tyler D. Cumby, D. S. Jin

Published Sep 2, 2009• 22 citations
arXivHTMLPDF

Abstract

We create atom-molecule superpositions in a Bose-Fermi mixture of $^{87}\text{R}\text{b}$ and $^{40}\text{K}$ 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.

DOI
10.1103/physreva.80.030701

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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 \ensuremathμs150\text{ }\ensuremath{\mu}\text{s}150 \ensuremathμs 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.
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.
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 test a non equilibrium approach to study the behavior of a Bose-Fermi mixture of alkali atoms in the presence of a Feshbach resonance between bosons and fermions. To this end we derive the Hartree-Fock-Bogoliubov (HFB) equations of motion for, the interacting system. This approach has proven very successful in the study of resonant systems composed of Bose particles and Fermi particles. However, when applied to a Bose-Fermi mixture, the HFB theory fails to identify even the correct binding energy of molecules in the appropriate limit. Through a more rigorous analysis we are able to ascribe this difference to the peculiar role that bosonic depletion plays in the Bose-Fermi pair correlation, which is the mechanism through which molecules are formed. We therefore conclude that molecular formation in Bose-Fermi mixtures is driven by three point and higher order correlations in the gas, unlike any other resonant system studied in the context of ultra-cold atomic physics.
Theoretical treatments of nonequilibrium dynamics in strongly interacting Bose-Fermi mixtures are complicated by the inherent non-Gaussian nature of the vacuum two-body physics, invalidating the typical Hartree-Fock-Bogoliubov approximation. Here we apply the cumulant expansion to study nonequilibrium Bose-Fermi mixtures, which allows us to explicitly include the missing non-Gaussian quantum correlations, leading to a consistent dynamical theory of a Bose-Fermi mixture near an interspecies Feshbach resonance. We first apply our theory to a study of atom-pair coherence in the gas, which is significantly enhanced by the competing influences of the Fermi sea and Bose-Einstein condensation, in agreement with analytical calculations. Then we study the depletion of a degenerate Bose-Fermi mixture following a quench to the unitary regime, characterizing the resulting depletion of the Bose-Einstein condensate, the deformation of the Fermi surface, and the production of molecules. We find that at early times, the population dynamics scale quadratically with the hold time, and define an associated characteristic timescale set by the parameters of the mixture and the width of the Feshbach resonance. Published by the American Physical Society 2024
We report on the creation of heterospecies bosonic molecules, associated from an ultracold Bose-Bose mixture of 41K^{41}\mathrm{K}41K and 87Rb^{87}\mathrm{Rb}87Rb, by using a resonantly modulated magnetic field close to two Feshbach resonances. We measure the binding energy of the weakly bound molecular states versus the Feshbach field and compare our results to theoretical predictions. We observe the broadening and asymmetry of the association spectrum due to the thermal distribution of the atoms and a frequency shift occurring when the binding energy depends nonlinearly on the Feshbach field. A simple model is developed to quantitatively describe the association process. This work represents a required step toward Bose-Einstein condensates of dipolar molecules.