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arXiv:2005.01277 · Physical Review Research

Full-dimensional quantum scattering calculations on ultracold atom-molecule collisions in magnetic fields: The role of molecular vibrations

Masato Morita, Jacek A. Kłos, Timur V. Tscherbul

Published Nov 30, 2020• 12 citations
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Abstract

The authors present quantum dynamics calculations on strongly anisotropic Li + CaH collisions at ultralow temperatures in the presence of an external magnetic field, and show the role of vibrational degrees of freedom in determining the properties of magnetic Feshbach resonances in ultracold atom-molecule collisions.
DOI
10.1103/physrevresearch.2.043294

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Magnetic Feshbach resonances play a central role in experimental research on atomic gases at ultracold temperatures, as they allow one to control the microscopic interactions between ultracold atoms by tuning an applied magnetic field. These resonances arise due to strong hyperfine interactions between the unpaired electron and the nuclear magnetic moment of the alkali metal atoms. A major thrust of current research is to create an ultracold gas of diatomic alkali metal molecules in the ground rovibrational state of the ground electronic ${}^{1}\ensuremath{\Sigma}$ state. Unlike alkali metal atoms, ${}^{1}\ensuremath{\Sigma}$ diatomic molecules have no unpaired electrons. However, the hyperfine interactions of molecules may give rise to magnetic Feshbach resonances. We use quantum scattering calculations to study the possible width of these resonances. Our results show that the widths of magnetic Feshbach resonances in ultracold molecule-molecule collisions for ${}^{1}\ensuremath{\Sigma}$ molecules may exceed 1 mG, rendering such resonances experimentally detectable. We hope that this work will stimulate the experimental search of these resonances.
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Rigorous coupled-channel quantum scattering calculations on molecular collisions in external fields are computationally demanding due to the need to account for a large number of coupled channels and multiple total angular momenta J of the collision complex. We show that by restricting the total angular momentum basis to include only the states with helicities K ≤ Kmax, it is possible to obtain accurate elastic and inelastic cross sections for low-temperature He + CaH, Li + CaH, and Li + SrOH collisions in the presence of an external magnetic field at a small fraction of the computational cost of the full coupled-channel calculations (where K is the projection of the molecular rotational angular momentum on the atom-diatom axis). The optimal size of the truncated helicity basis set depends on the mechanism of the inelastic process and on the magnitude of the external magnetic field, with the minimal basis set (Kmax = 0) producing quantitatively accurate results for, e.g., ultracold Li + CaH and Li + SrOH scattering at low magnetic fields, leading to nearly 90-fold gain in computational efficiency. Larger basis sets are required to accurately describe the resonance structure in the magnetic field dependence of Li + CaH and Li + SrOH inelastic cross sections in the few partial wave-regime as well as indirect spin relaxation in He + CaH collisions. Our calculations indicate that the resonance structure is due to an interplay of the spin-rotation and Coriolis couplings between the basis states of different K and the couplings between the rotational states of the same K induced by the anisotropy of the interaction potential.