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arXiv:cond-mat/0410083 · Physical Review A

Feshbach spectroscopy of a shape resonance

Thomas Volz, Stephan Dürr, Niels Syassen, Gerhard Rempe, Eric van Kempen, S. J. J. M. F. Kokkelmans

Published Jul 29, 2005• 36 citations
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Abstract

We present a spectroscopy technique for studying cold-collision properties. The technique is based on the association and dissociation of ultracold molecules using a magnetically tunable Feshbach resonance. The energy and lifetime of a shape resonance are determined from a measurement of the dissociation rate. Additional spectroscopic information is obtained from the observation of a spatial interference pattern between an outgoing $s$ wave and $d$ wave. The experimental data agree well with the results from a model, in which the dissociation process is connected to a scattering gedanken experiment, which is analyzed using a coupled-channel calculation.

DOI
10.1103/physreva.72.010704

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We present a spectroscopy technique for studying cold-collision properties. The technique is based on the association and dissociation of ultracold molecules using a magnetically tunable Feshbach resonance. The energy and lifetime of a shape resonance are determined from a measurement of the dissociation rate. Additional spectroscopic information is obtained from the observation of a spatial interference pattern between an outgoing sss wave and ddd wave. The experimental data agree well with the results from a model, in which the dissociation process is connected to a scattering gedanken experiment, which is analyzed using a coupled-channel calculation.
Magnetically tunable Feshbach resonances were employed to associate cold diatomic molecules in a series of experiments involving both atomic Bose and two-spin-component Fermi gases. This review illustrates theoretical concepts of both the particular nature of the highly excited Feshbach molecules produced and the techniques for their association from unbound atom pairs. Coupled-channels theory provides a rigorous formulation of the microscopic physics of Feshbach resonances in cold gases. Concepts of dressed versus bare energy states, universal properties of Feshbach molecules, and the classification in terms of entrance- and closed-channel-dominated resonances are introduced on the basis of practical two-channel approaches. Their significance is illustrated for several experimental observations, such as binding energies and lifetimes with respect to collisional relaxation. Molecular association and dissociation are discussed in the context of techniques involving linear magnetic-field sweeps in cold Bose and Fermi gases and pulse sequences leading to Ramsey-type interference fringes. Their descriptions in terms of Landau-Zener, two-level mean-field, as well as beyond mean-field approaches are reviewed in detail, including the associated ranges of validity.
We have observed and located more than 60 magnetic field-induced Feshbach resonances in ultracold collisions of ground-state 133Cs^{133}\mathrm{Cs}133Cs atoms. Multiple extremely weak Feshbach resonances associated with ggg-wave molecular states are detected through variations in the radiative collision cross sections. The Feshbach spectroscopy allows us to determine the interactions between ultracold cesium atoms and the molecular energy structure near the dissociation continuum with unprecedented precision. Our work not only represents a very successful collaboration of experimental and theoretical efforts, but also provides essential information for cesium Bose-Einstein condensation, Cs2{\mathrm{Cs}}_{2}Cs2​ molecules, and atomic clock experiments.
Ultracold molecules can be associated from ultracold atoms by ramping the magnetic field through a Feshbach resonance. A reverse ramp dissociates the molecules. Under suitable conditions, more than one outgoing partial wave can be populated. A theoretical model for this process is discussed here in detail. The model reveals the connection between the dissociation and the theory of multichannel scattering resonances. In particular, the decay rate, the branching ratio, and the relative phase between the partial waves can be predicted from theory or extracted from experiment. The results are applicable to our recent experiment in 87Rb^{87}\mathrm{Rb}87Rb, which has a ddd-wave shape resonance.
Ultracold molecules are associated from an atomic Bose-Einstein condensate by ramping a magnetic field across a Feshbach resonance. The reverse ramp dissociates the molecules. The kinetic energy released in the dissociation process is used to measure the widths of four Feshbach resonances in 87Rb^{87}\mathrm{Rb}87Rb. This method to determine the width works remarkably well for narrow resonances even in the presence of significant magnetic-field noise. In addition, a quasimonoenergetic atomic wave is created by jumping the magnetic field across the Feshbach resonance.