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arXiv:0812.1233 · Faraday Discussions

Ultracold molecules from ultracold atoms: a case study with the KRb molecule

Paul S. Julienne

Published Jan 1, 2009• 54 citations
arXivHTMLPDF

Abstract

Ultracold collisions of cold atoms or molecules make the bound states of the collision complex formed from the two colliding species accessible for control and manipulation of the cold species or the complex. Such resonances are best treated by a resonant scattering theory, which in the ultracold domain can take advantage of the properties of the long-range potential and the methods of multichannel quantum defect theory. Coupled channels calculations on the threshold scattering states and bound states of the 40K87Rb molecule illustrate the ideas and methodology of quantum defect theory using the long-range potential and also demonstrate the spin properties of the bound states throughout the spectrum.

DOI
10.1039/b820917k

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Ultracold molecules from ultracold atoms: a case study with the KRb molecule

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Ultracold collisions of cold atoms or molecules make the bound states of the collision complex formed from the two colliding species accessible for control and manipulation of the cold species or the complex. Such resonances are best treated by a resonant scattering theory, which in the ultracold domain can take advantage of the properties of the long-range potential and the methods of multichannel quantum defect theory. Coupled channels calculations on the threshold scattering states and bound states of the 40K87Rb molecule illustrate the ideas and methodology of quantum defect theory using the long-range potential and also demonstrate the spin properties of the bound states throughout the spectrum.
Ultracold collisions of cold atoms or molecules make the bound states of the collision complex formed from the two colliding species accessible for control and manipulation of the cold species or the complex. Such resonances are best treated by a resonant scattering theory, which in the ultracold domain can take advantage of the properties of the long-range potential and the methods of multichannel quantum defect theory. Coupled channels calculations on the threshold scattering states and bound states of the 40 K 87 Rb molecule illustrate the ideas and methodology of quantum defect theory using the long-range potential and also demonstrate the spin properties of the bound states throughout the spectrum. 1
A simple quantum-defect model gives analytic expressions for the complex scattering length and threshold collision rates of ultracold molecules. If the probability of reaction in the short-range part of the collision is high, the model gives universal rate constants for s- and p-wave collisions that are independent of short-range dynamics. This model explains the magnitudes of the recently measured rate constants for collisions of two ultracold 40K87Rb molecules, or an ultracold 40K atom with the 40K87Rb molecule [S. Ospelkaus et al., Science 327, 853 (2010).
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.
There is great interest in the production of cold molecules, at temperatures below 1 K, and ultracold molecules, at temperatures below 1 mK. Such molecules have potential applications in areas ranging from precision measurement to quantum information storage and processing, and quantum gases of ultracold polar molecules are expected to exhibit novel quantum phases. In addition, cold molecules open up a new domain for collision physics, dominated by long-range forces and scattering resonances. There have been major recent advances both in cooling molecules from room temperature and in forming molecules in ultracold atomic gases. As these techniques mature, and cold and ultracold samples are more accessible, collision studies at previously unavailable energies will be possible. This spotlight article will highlight some of the background and motivation for studying collisions at low energies and will direct readers to recent articles on the recent experimental advancements.
We develop an analytical model for ultracold atom–ion collisions using the multichannel quantum-defect formalism. The model is based on analytical solutions of the r −4 long-range potential and on the application of a frame transformation between asymptotic and molecular bases. This approach allows the description of atom–ion interaction in the ultracold domain in terms of only three parameters: the singlet and triplet scattering lengths, assumed to be independent of the relative motion angular momentum, and the lead dispersion coefficient of the asymptotic potential. We also introduce corrections to the scattering lengths that improve the accuracy of our quantum-defect model for higher-order partial waves, a particularly important result for an accurate description of shape and Feshbach resonances at finite temperature. The theory is applied to the system composed of a 40 Ca + ion and a Na atom, and compared with numerical coupled-channel calculations carried out using ab initio potentials. For this particular system, we investigate the spectrum of bound states, the rate of charge-transfer processes and the collision rates in the presence of magnetic Feshbach resonances at zero and finite temperature.
This chapter summarizes the properties of near-threshold molecular states that can be formed from ultracold atoms. The properties of the states for a single potential are characterized for different partial waves using the concepts of quantum defect theory for a van der Waals potential. Examples are given for various isotopes of the Yb_2 molecule. Magnetically tunable Feshbach resonances or photoassociation resonances are characterized by the multichannel version of the theory. Examples of the latter are given for the KRb molecule.