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arXiv:1104.5600 · New Journal of Physics

Multichannel quantum-defect theory for ultracold atom–ion collisions

Zbigniew Idziaszek, Andrea Simoni, Tommaso Calarco, Paul S. Julienne

Published Aug 8, 2011• 81 citations
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Abstract

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.

DOI
10.1088/1367-2630/13/8/083005

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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.
We study atom-ion scattering in the ultracold regime. To this aim, an analytical model based on the multichannel quantum-defect formalism is developed and compared to close-coupled numerical calculations. We investigate the occurrence of magnetic Feshbach resonances, focusing on the specific 40Ca++Na^{40}\mathrm{Ca}^{+}+\mathrm{Na}40Ca++Na system. The presence of several resonances at experimentally accessible magnetic fields should allow the atom-ion interaction to be precisely tuned. A fully quantum-mechanical study of charge-exchange processes shows that charge-exchange rates should remain small even in the presence of resonance effects. Most of our results can be cast in a system-independent form and are important for the realization of charge-neutral ultracold systems.
We present a multichannel quantum-defect theory for slow atomic collisions that takes advantages of the analytic solutions for the long-range potential and both the energy and angular momentum insensitivities of the short-range parameters. The theory provides an accurate and complete account of scattering processes, including shape and Feshbach resonances, in terms of a few parameters such as the singlet and triplet scattering lengths. As an example, results for $^{23}\mathrm{Na}\ensuremath{-}^{23}\mathrm{Na}$ scattering are presented and compared to close-coupling calculations.
We present analytic descriptions of atomic interaction at ultracold temperatures using both single-channel and multichannel quantum-defect theories. In the case of a single channel, addressed in this paper, the expansion of Gao [Phys. Rev. A 58, 4222 (1998)] is generalized to higher orders for angular momentum $l\ensuremath{\ge}2$ to give a more complete description of ultracold scattering, including an analytic description of ultracold shape resonances of arbitrary lll. We also introduce a generalized scattering length that is well defined and useful for all partial waves to replace the traditional definition that fails for $l\ensuremath{\ge}2$ due to the long-range van der Waals interaction. The results are used in a companion paper to derive analytic descriptions of atomic interaction around a magnetic Feshbach resonance of arbitrary angular momentum lll.
We present a theoretical model for describing ultracold atomic collision based on the multichannel quantum-defect theory. An analytical expression for the quantum-defect matrix Y is derived for the truncated 1/R61/{R}^{6}1/R6 model potential, and threshold behaviors of the quantum-defect parameters are discussed. The model allows us to predict the Feshbach resonances when the singlet and triplet scattering lengths are known or to fit the scattering lengths when a couple of Feshbach resonances is located experimentally. As an illustrative example, we investigate the 6{}^{6}6Li-40{}^{40}40K scattering. The theoretical results agree quite well with experimental values.
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.