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Exploring Exotic Atomic and Molecular Collisions at Ultracold Temperatures

Brandon Ruzic

Published Jan 1, 2015• 0 citations
OpenAlex

Abstract

New experimental techniques have increased the scope of atomic and molecular control at ultracold temperatures. To understand molecular collisions and collisions between atoms with large electronic spin, we extend multichannel quantum defect theory to describe scattering in the case of high-partial-wave angular momentum and long-range anisotropic interactions. The efficiency and accuracy of these calculations facilitate the prediction and characterization of Fano-Feshbach resonances.

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New experimental techniques have increased the scope of atomic and molecular control at ultracold temperatures. To understand molecular collisions and collisions between atoms with large electronic spin, we extend multichannel quantum defect theory to describe scattering in the case of high-partial-wave angular momentum and long-range anisotropic interactions. The efficiency and accuracy of these calculations facilitate the prediction and characterization of Fano-Feshbach resonances.
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.
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 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 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 introduce a choice of reference wave functions that allows multichannel quantum defect theory (MQDT) to describe ultracold collisions involving high-partial-wave quantum numbers LLL. This requires a careful standardization of the MQDT reference wave functions at long range to ensure their linear independence. To illustrate the simplicity and accuracy of the resulting theory, we perform a comprehensive calculation of $L\ensuremath{\le}2$ Fano-Feshbach resonances in the range 0−−10000--10000−−1000 G for the scattering of 40K+87Rb{}^{40}\mathrm{K}{+}^{87}\mathrm{Rb}40K+87Rb in their lowest hyperfine states. Moreover, we derive analytic expressions for our universal set of MQDT parameters in the threshold regime.
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.