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arXiv:0902.1727

Molecular States Near a Collision Threshold

Paul S. Julienne

Published Jun 25, 2009• 1 citation
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Abstract

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.

DOI
10.1201/9781420059045-14

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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.
Magnetically tunable scattering resonances have been used with great success for precise control of s-wave scattering lengths in ultracold atomic collisions. We describe relatively simple yet quite powerful analytic treatments of such resonances based on the analytic properties of the van der Waals long range potential. This theory can be used to characterize a number of properties of specific resonances that have been used successfully in various experiments with 87^{87}87Rb, 85^{85}85Rb, 40^{40}40K, and 6^{6}6Li. Optical Feshbach resonances are also possible and may be practical with narrow intercombination line photoassociative transitions in species like Sr and Yb.
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
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.
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.
Magnetically tunable scattering resonances have been used with great success for precise control of s‐wave scattering lengths in ultracold atomic collisions. We describe relatively simple yet quite powerful analytic treatments of such resonances based on the analytic properties of the van der Waals long range potential. This theory can be used to characterize a number of properties of specific resonances that have been used successfully in various experiments with 87Rb, 85Rb, 40K, and 6Li. Optical Feshbach resonances are also possible and may be practical with narrow intercombination line photoassociative transitions in species like Sr and Yb.