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Inelastic collisions of atomic antimony, aluminum, erbium and thulium below 1 K

Colin B. Connolly

Published Nov 15, 2012• 2 citations
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Abstract

Inelastic collision processes driven by anistropic interactions are investigated below 1 K. Three distinct experiments are presented. First, for the atomic species antimony (Sb), rapid relaxation is observed in collisions with \\(^4He\\). We identify the relatively large spin-orbit coupling as the primary mechanism which distorts the electrostatic potential to introduce significant anisotropy to the ground \\(^4S_{3/2}\\) state. The collisions are too rapid for the experiment to fix a specific value, but an upper bound is determined, with the elastic-to-inelastic collision ratio \\(\\gamma \\leq 9.1 x 10^2\\). In the second experiment, inelastic \\(\\mathcal{m}_J\\)-changing and \\(J\\)-changing transition rates of aluminum (Al) are measured for collisions with \\(^3He\\). The experiment employs a clean method using a single pump/probe laser to measure the steady-state magnetic sublevel population resulting from the competition of optical pumping and inelastic collisions. The collision ratio \\(\\gamma\\) is measured for both \\(\\mathcal{m}_J\\)- and \\(J\\)-changing processes as a function of magnetic field and found to be in agreement with the theoretically calculated dependence, giving support to the theory of suppressed Zeeman relaxation in spherical \\(^2P_{1/2}\\) states [1]. In the third experiment, very rapid atom-atom relaxation is observed for the trapped lanthanide rare-earth atoms erbium (Er) and thulium (Tm). Both are nominally nonspherical \\((L \\neq 0)\\) atoms that were previously observed to have strongly suppressed electronic interaction anisotropy in collisions with helium \\((\\gamma > 10^4-10^5, [2,3])\\). No suppression is observed in collisions between these atoms \\((\\gamma \\lesssim 10)\\), which likely implies that evaporative cooling them in a magnetic trap will be impossible. Taken together, these studies reveal more of the role of electrostatic anisotropy in cold atomic collisions.

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Physical Review A•Oct 17, 2008•14 citations
Inelastic collision processes driven by anistropic interactions are investigated below 1 K. Three distinct experiments are presented. First, for the atomic species antimony (Sb), rapid relaxation is observed in collisions with \(^4He\). We identify the relatively large spin-orbit coupling as the primary mechanism which distorts the electrostatic potential to introduce significant anisotropy to the ground \(^4S_{3/2}\) state. The collisions are too rapid for the experiment to fix a specific value, but an upper bound is determined, with the elastic-to-inelastic collision ratio \(\gamma \leq 9.1 x 10^2\). In the second experiment, inelastic \(\mathcal{m}_J\)-changing and \(J\)-changing transition rates of aluminum (Al) are measured for collisions with \(^3He\). The experiment employs a clean method using a single pump/probe laser to measure the steady-state magnetic sublevel population resulting from the competition of optical pumping and inelastic collisions. The collision ratio \(\gamma\) is measured for both \(\mathcal{m}J\)- and \(J\)-changing processes as a function of magnetic field and found to be in agreement with the theoretically calculated dependence, giving support to the theory of suppressed Zeeman relaxation in spherical \(^2P{1/2}\) states [1]. In the third experiment, very rapid atom-atom relaxation is observed for the trapped lanthanide rare-earth atoms erbium (Er) and thulium (Tm). Both are nominally nonspherical \((L \neq 0)\) atoms that were previously observed to have strongly suppressed electronic interaction anisotropy in collisions with helium \((\gamma > 10^4-10^5, [2,3])\). No suppression is observed in collisions between these atoms \((\gamma \lesssim 10)\), which likely implies that evaporative cooling them in a magnetic trap will be impossible. Taken together, these studies reveal more of the role of electrostatic anisotropy in cold atomic collisions.
We present a quantitative study of suppression of cold inelastic collisions by the spin-orbit interaction. We prepare cold ensembles of >10(11) Al(2P(1/2)) atoms via cryogenic buffer-gas cooling and use a single-beam optical pumping method to measure their magnetic (m(J)-changing) and fine-structure (J-changing) collisions with 3He atoms at millikelvin temperatures over a range of magnetic fields from 0.5 to 6 T. The experimentally determined rates are in good agreement with the functional form predicted by quantum scattering calculations using ab initio potentials. This comparison provides direct experimental evidence for a proposed model of suppressed inelasticity in collisions of atoms in 2P(1/2) states [T. V. Tscherbul et al., Phys. Rev. A 80, 040701(R) (2009)], which may allow for sympathetic cooling of other 2P(1/2) atoms (e.g., In, Tl and metastable halogens).
We investigate Zeeman relaxation in cold Sb(${}^{4}{S}_{3/2}^{\ensuremath{\circ}}$)--He collisions in a magnetic field. Ensembles of >>>1013{10}^{13}1013 laser-ablated Sb atoms are cooled in cryogenic 4{}^{4}4He buffer gas to 800 mK and inelastic collisions are observed to equilibrate the mJ{m}_{J}mJ​-state distribution to the translational temperature. The ratio $\ensuremath{\gamma}$ of momentum transfer to inelastic collision rates is measured to be $\ensuremath{\leqslant}9.1\ifmmode\times\else\texttimes\fi{}{10}^{2}$. We also perform quantum scattering calculations of Sb--4{}^{4}4He collisions, based on ab initio interaction potentials, that demonstrate significant anisotropy of the ground state induced by the spin-orbit interaction. Agreement is obtained between theory and experiment with a $\ensuremath{\approx}101010%$ increase in the ab initio potential depth. This work suggests that buffer-gas-cooled pnictogen atoms lighter than Sb can be loaded into a magnetic trap.
Spin relaxation due to atom--atom collisions is measured for magnetically trapped erbium and thulium atoms at a temperature near 500 mK. The rate constants for Er--Er and Tm--Tm collisions are $3.0\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10}$ and $1.1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10}$ cm3{}^{3}3 ${\mathrm{s}}^{\ensuremath{-}1}$, respectively, 2−−32--32−−3 orders of magnitude larger than those observed for highly magnetic SSS-state atoms. This is strong evidence for an additional, dominant, spin relaxation mechanism, electronic interaction anisotropy, in collisions between these ``submerged-shell,'' $L\ensuremath{\ne}0$ atoms. These large spin relaxation rates imply that evaporative cooling of these atoms in a magnetic trap will be highly inefficient.
We present a combined experimental and theoretical study of cold collisions between bismuth and helium atoms in strong magnetic fields and demonstrate that the spin-orbit interaction coupling between different nonrelativistic states of Bi leads to rapid Zeeman relaxation. The Zeeman relaxation of Bi in the ground electronic state is found to be very efficient due to the admixture of electronic excited states which show an interaction anisotropy due to their nonzero electronic orbital angular momentum. Our results indicate that dense ensembles of heavy relativistic atoms will generally be unstable in magnetic traps due to significant spin relaxation induced by spin-orbit interactions.
The binary collision dynamics of 2Dg,3/2{}^{2}{D}_{g,3/2}2Dg,3/2​ ground state scandium atoms is studied from first principles. We employ 30 coupled diabatic ab initio potentials in a coupled-channels study of the scattering dynamics of cold and ultracold scandium atoms in external magnetic fields. Due to the long-ranged magnetic dipolar interaction, the field dependence of the cross section does not follow the threshold laws derived by Volpi and Bohn [Phys. Rev. A 65, 052712 (2002)]. In the field-free case, the near-threshold cross section is independent of the collision energy, and hence the cross section does not follow the well-established Wigner threshold laws. The observed threshold behavior is explained in the Born approximation. For energies above $1\phantom{\rule{4pt}{0ex}}\ensuremath{\mu}\mathrm{K}$, inelastic collisions are driven by the anisotropic nonrelativistic electronic interaction. For energies below $100\phantom{\rule{4pt}{0ex}}\ensuremath{\mu}\mathrm{K}$, the ratio of elastic-to-inelastic collisions is likely to be favorable for evaporative cooling. Both anisotropy in the long-range interaction and in the short-range potential contribute to large cross sections for inelastic collisions at higher energies and lead to a small ratio of elastic-to-inelastic collisions. This is in agreement with the large rates for Zeeman relaxation of submerged-shell atoms observed experimentally. The effect of the uncertainty in the ab initio potential is sampled by scaling the reduced mass and is found to have little influence on the conclusions drawn from this work.
We present a combined experimental and theoretical study of cold collisions between bismuth and helium atoms in strong magnetic fields and demonstrate that the spin-orbit interaction coupling between different nonrelativistic states of Bi leads to rapid Zeeman relaxation. The Zeeman relaxation of Bi in the ground electronic state is found to be very efficient due to the admixture of electronic excited states which show an interaction anisotropy due to their nonzero electronic orbital angular momentum. Our results indicate that dense ensembles of heavy relativistic atoms will generally be unstable in magnetic traps due to significant spin relaxation induced by spin-orbit interactions.