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Physical Review A

Feshbach resonances in ultracold atom-diatom scattering

Robert C. Forrey, N. Balakrishnan, Vasili A. Kharchenko, A. Dalgarno

Published Oct 1, 1998• 59 citations
Publisher

Abstract

Quantum-mechanical scattering calculations of Feshbach resonances arising from van der Waals molecule formation are used to determine vibrational and rotational predissociation lifetimes. A multichannel effective range theory is used to establish the relationship between predissociation and the zero-temperature limit of collisional quenching for resonances lying close to the thresholds for dissociation. The elastic scattering Feshbach resonances may be measurable in ultracold atom-molecule experiments.

DOI
10.1103/physreva.58.r2645

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Quantum-mechanical scattering calculations of Feshbach resonances arising from van der Waals molecule formation are used to determine vibrational and rotational predissociation lifetimes. A multichannel effective range theory is used to establish the relationship between predissociation and the zero-temperature limit of collisional quenching for resonances lying close to the thresholds for dissociation. The elastic scattering Feshbach resonances may be measurable in ultracold atom-molecule experiments.
We study the rotational predissociation of atom-molecule complexes with very small binding energy. Such complexes can be produced by Feshbach resonance association of ultracold molecules with ultracold atoms. Numerical calculations of the predissociation lifetimes based on the computation of the energy dependence of the scattering matrix elements become inaccurate when the binding energy is smaller than the energy width of the predissociating state. We derive expressions that represent accurately the predissociation lifetimes in terms of the real and imaginary parts of the scattering length and effective range for molecules in an excited rotational state. Our results show that the predissociation lifetimes are the longest when the binding energy is positive, i.e., when the predissociating state is just above the excited state threshold.
We review the recent progress achieved in the theoretical description of chemical reactions at low temperatures. In particular, we discuss the crucial role played by the van der Waals interaction potential in quantum-mechanical scattering calculations of atom–diatom collisions in the cold and ultracold regimes, where abstraction reactions proceed by tunnelling. The importance of zero-energy resonances in enhancing the reactivity in the zero-temperature limit is assessed. The impact of Feshbach resonances associated with the decay of metastable states of van der Waals complexes on reactive scattering is addressed through a series of examples. Finally, we discuss the sensitivity of the reaction dynamics to the topology of the van der Waals well. Importance of long-range interactions in chemical reactions at cold and ultracold temperaturesAll authorsPhilippe F. Weck & N. Balakrishnanhttps://doi.org/10.1080/01442350600791894Published online:22 February 2007Table Download CSVDisplay Table
Compared to purely atomic collisions, ultracold collisions involving molecules have the potential to support a much larger number of Fano-Feshbach resonances due to the huge amount of ro-vibrational states available. In order to handle such ultracold atom-molecule collisions, we formulate a theory that incorporates the ro-vibrational Fano-Feshbach resonances in a statistical manner while treating the physics of the long-range scattering, which is sensitive to such things as hyperfine states, collision energy, and any applied electromagnetic fields, exactly within multichannel quantum defect theory. Uniting these two techniques, we can assess the influence of highly resonant scattering in the threshold regime, and in particular its dependence on the hyperfine state selected for the collision. This allows us to explore the onset of Ericson fluctuations in the regime of overlapping resonances, which are well known in nuclear physics but completely unexplored in the ultracold domain.
Vibrational relaxation of trapped molecules due to collisions with cold atoms is investigated using the results of quantum-mechanical scattering calculations. Trap loss is analyzed using an exactly solvable kinetic model that includes direct collisional quenching and an indirect process of vibrational predissociation. At low atom density, the relaxation is due primarily to collisional quenching. At high atom density, the relaxation involves additional time scales due to the formation and decay of van der Waals complexes. It is shown that the most weakly bound state of the van der Waals complex for a given diatomic vibrational level controls the relaxation at all atom densities. Possible experiments using trapped molecules are discussed.
We have developed a model of Feshbach resonances in gases of ultracold alkali-metal atoms using the ideas of multichannel quantum-defect theory. Our model requires just three parameters describing the interactions---the singlet and triplet scattering lengths, and the long-range van der Waals coefficient---in addition to known atomic properties. Without using any further details of the interactions, our approach can accurately predict the locations of resonances. It can also be used to find the singlet and triplet scattering lengths from measured resonance data. We apply our technique to 6Li-40K^{6}\text{L}\text{i-}^{40}\text{K}6Li-40K and $^{40}\text{K}\text{\ensuremath{-}}^{87}\text{R}\text{b}$ scattering, obtaining good agreement with experimental results, and with the more computationally intensive coupled channels technique.
We study the spontaneous dissociation of diatomic molecules produced in cold atomic gases via magnetically tunable Feshbach resonances. We provide a universal formula for the lifetime of these molecules that relates their decay to the scattering length and the loss rate constant for inelastic spin relaxation. Our universal treatment as well as our exact coupled channels calculations for 85Rb dimers predict a suppression of the decay over several orders of magnitude when the scattering length is increased. Our predictions are in good agreement with recent measurements of the lifetime of 85Rb(2).