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arXiv:1904.01281 · Physical Review A

Ultracold homonuclear and heteronuclear collisions in metastable helium

Daniel Cocks, Ian B. Whittingham, G. Peach

Published Jun 28, 2019• 4 citations
arXivHTMLPDF

Abstract

Scattering and ionizing cross sections and rates are calculated for ultracold collisions between metastable helium atoms using a fully quantum-mechanical close-coupled formalism. Homonuclear collisions of the bosonic $^{4}\mathrm{He}^{*}+^{4}\mathrm{He}^{*}$ and fermionic $^{3}\mathrm{He}^{*}+^{3}\mathrm{He}^{*}$ systems, and heteronuclear collisions of the mixed $^{3}\mathrm{He}^{*}+^{4}\mathrm{He}^{*}$ system, are investigated over the temperature range 1 $\ensuremath{\mu}\mathrm{K}$ to 1 K. Carefully constructed Born-Oppenheimer molecular potentials are used to describe the electrostatic interaction between the colliding atoms, and complex optical potentials to represent loss through ionization from the ${}^{1,3}\mathrm{\ensuremath{\Sigma}}$ states. Magnetic spin-dipole-mediated transitions from the ${}^{5}\mathrm{\ensuremath{\Sigma}}$ state are included and results reported for spin-polarized and unpolarized systems. Comparisons are made with experimental results, previous semiclassical models, and a perturbed single-channel model.

DOI
10.1103/physreva.99.062712

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We present a theoretical and experimental investigation of homonuclear ionizing collisions of laser-cooled metastable (23S1)(2\phantom{\rule{0.2em}{0ex}}^{3}S_{1})(23S1​) helium atoms, considering both the fermionic 3He^{3}\mathrm{He}3He and bosonic 4He^{4}\mathrm{He}4He isotopes. The theoretical description combines quantum threshold behavior, Wigner's spin-conservation rule, and quantum-statistical symmetry requirements in a single-channel model, complementing a more complete close-coupling theory that has been reported for collisions of metastable 4He^{4}\mathrm{He}4He atoms. The model is supported with measurements (in the absence of light fields) of ionization rates in magneto-optically trapped samples that contain about $3\ifmmode\times\else\texttimes\fi{}{10}^{8}$ atoms of a single isotope. The ionization rates are determined from measurements of trap loss due to light-assisted collisions combined with comparative measurements of the ion production rate in the absence and presence of trapping light. Theory and experiment show good agreement.
A quantum-mechanical close-coupled calculation for collisions of spin-polarized triplet helium atoms in a magnetostatic trap is presented in which the Penning and associative ionization processes are represented by a complex optical potential. The rate coefficients for the spin relaxation and relaxation-induced Penning ionization processes for a range of magnetic fields and temperatures, spanning the cold and ultracold temperature regimes, have been calculated and the sensitivity of these results to uncertainties in the molecular potentials and autoionization width investigated. The rate constants for both elastic and inelastic processes were found to be particularly sensitive to the short-range ${}^{5}{\ensuremath{\Sigma}}_{g}^{+}$ molecular potential and, to a lesser extent, the rate constants for relaxation-induced Penning ionization displayed sensitivity to the short-range form of the ${}^{1}{\ensuremath{\Sigma}}_{g}^{+}$ molecular potential and the autoionization width.
We report scattering lengths for the ${}^{1}{\ensuremath{\Sigma}}_{g}^{+},$ ${}^{3}{\ensuremath{\Sigma}}_{u}^{+},$ and ${}^{5}{\ensuremath{\Sigma}}_{g}^{+}$ adiabatic molecular potentials relevant to collisions of two metastable 23S2{}^{3}S23S helium atoms as a function of the uncertainty in these potentials. These scattering lengths are used to calculate experimentally observable scattering lengths, elastic cross sections, and inelastic rates for any combination of states of the colliding atoms, at temperatures where the Wigner threshold approximation is valid.
We have investigated cold ionizing heteronuclear collisions in dilute mixtures of metastable (23S1)(2\phantom{\rule{0.2em}{0ex}}^{3}S_{1})(23S1​) 3He^{3}\mathrm{He}3He and 4He^{4}\mathrm{He}4He atoms, extending our previous work on the analogous homonuclear collisions [R. J. W. Stas et al., Phys. Rev. A 73, 032713 (2006)]. A simple theoretical model of such collisions enables us to calculate the heteronuclear ionization rate coefficient, for our quasiunpolarized gas, in the absence of resonant light (T=1.2mK)(T=1.2\phantom{\rule{0.2em}{0ex}}\mathrm{mK})(T=1.2mK): ${K}_{34}^{(\mathrm{th})}=2.4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10}\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{3}∕\mathrm{s}$. This calculation is supported by a measurement of K34{K}_{34}K34​ using magneto-optically trapped mixtures containing about $1\ifmmode\times\else\texttimes\fi{}{10}^{8}$ atoms of each species, ${K}_{34}^{(\mathrm{exp})}=2.5(8)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10}\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{3}∕\mathrm{s}$. Theory and experiment show good agreement.
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A quantum-mechanical close-coupled calculation of field-free collisions of cold metastable helium atoms has been performed. Theoretical predictions of the rate coefficients for elastic processes and losses due to the Penning and associative ionization processes are reported for temperatures ranging from 1 $\ensuremath{\mu}\mathrm{K}$ to 1 K. The sensitivity of the rate constants to uncertainties in the molecular potentials and autoionization widths has been investigated. The total ionization loss rates were found to be sensitive to the short-range form of the ${}^{1}{\ensuremath{\Sigma}}_{g}^{+}$ molecular potential and the autoionization widths, while the total elastic rate constants exhibit greater sensitivity to the short-range ${}^{5}{\ensuremath{\Sigma}}_{g}^{+}$ molecular potential.