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arXiv:0909.0249 · Physical Review A

Large spin relaxation rates in trapped submerged-shell atoms

Colin B. Connolly, Yat Shan Au, S. Charles Doret, Wolfgang Ketterle, John M. Doyle

Published Jan 20, 2010• 38 citations
arXivHTMLPDF

Abstract

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 $1.1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10}$ cm${}^{3}$ ${\mathrm{s}}^{\ensuremath{-}1}$, respectively, $2--3$ orders of magnitude larger than those observed for highly magnetic $S$-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.

DOI
10.1103/physreva.81.010702

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arXiv:0705.0713•Physical Review Letters•Nov 30, 2007•13 citations
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×\else\texttimes\fi10\ensuremath−103.0\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10}3.0\ifmmode×\else\texttimes\fi10\ensuremath−10 and 1.1\ifmmode×\else\texttimes\fi10\ensuremath−101.1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10}1.1\ifmmode×\else\texttimes\fi10\ensuremath−10 cm3{}^{3}3 s\ensuremath−1{\mathrm{s}}^{\ensuremath{-}1}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≠0L\ensuremath{\ne}0L\ensuremath=0 atoms. These large spin relaxation rates imply that evaporative cooling of these atoms in a magnetic trap will be highly inefficient.
The collisional magnetic reorientation rate constant gR{g}_{R}gR​ is measured for magnetically trapped atomic dysprosium (Dy), an atom with large magnetic dipole moments. Using buffer gas cooling with cold helium, large numbers (>1011>{10}^{11}>1011) of Dy are loaded into a magnetic trap and the buffer gas is subsequently removed. The decay of the trapped sample is governed by collisional reorientation of the atomic magnetic moments. We find ${g}_{R}=1.9\ifmmode\pm\else\textpm\fi{}0.5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}11}$ cm3{}^{3}3 s${}^{\ensuremath{-}1}$ at 390 mK. We also measure the magnetic reorientation rate constant of holmium (Ho), another highly magnetic atom, and find ${g}_{R}=5\ifmmode\pm\else\textpm\fi{}2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}12}$ cm3{}^{3}3 ${\mathrm{s}}^{\ensuremath{-}1}$ at 690 mK. The Zeeman relaxation rates of these atoms are greater than expected for the magnetic dipole-dipole interaction, suggesting that another mechanism, such as an anisotropic electrostatic interaction, is responsible. Comparison with estimated elastic collision rates suggests that Dy is a poor candidate for evaporative cooling in a magnetic trap.
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.
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.
For the first time ultra-cold thulium atoms were trapped in a magnetic quadrupole trap with a small field gradient (20 Gs cm -1 ). The atoms were loaded from a cloud containing 4 × 10 5 atoms that were preliminarily cooled in a magneto-optical trap to the sub-Doppler temperature of 80 μK. As many as 4 × 10 4 atoms were trapped in the magnetic trap at the temperature of 40 μK. By the character of trap population decay the lifetime of atoms was determined (0.5 s) and an upper estimate was obtained for the rate constant of inelastic binary collisions for spin-polarised thulium atoms in the ground state (g in < 10 -11 cm 3 s -1 ).
The dynamics of magnetic relaxation of Tm atoms in cold helium gas is investigated using ab initio interaction potentials between Tm(2F)\mathrm{Tm}(^{2}F)Tm(2F) and He atoms. The interaction of Tm(2F)\mathrm{Tm}(^{2}F)Tm(2F) with He gives rise to four adiabatic potentials of ${\ensuremath{\Sigma}}^{+}$, $\ensuremath{\Pi}$, $\ensuremath{\Delta}$, and $\ensuremath{\Phi}$ symmetries, which are found to be degenerate to within $0.1\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$ at all interatomic distances larger than R=5.4A˚R=5.4\phantom{\rule{0.3em}{0ex}}\mathrm{\AA{}}R=5.4A˚. The small splitting between the interaction potentials leads to suppression of Zeeman transitions in Tm-He collisions. Our quantum scattering calculations yield a small rate constant of $1.5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}15}\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{3}\phantom{\rule{0.2em}{0ex}}{\mathrm{s}}^{\ensuremath{-}1}$ for Zeeman relaxation of the Tm(2F7∕2)\mathrm{Tm}(^{2}F_{7∕2})Tm(2F7∕2​) atoms in the maximally stretched M=7∕2M=7∕2M=7∕2 sublevel at the temperature 0.8K0.8\phantom{\rule{0.3em}{0ex}}\mathrm{K}0.8K, in reasonable agreement with the measured value $(5.0\ifmmode\pm\else\textpm\fi{}2.1)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}15}\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{3}\phantom{\rule{0.2em}{0ex}}{\mathrm{s}}^{\ensuremath{-}1}$. The sensitivity of Zeeman-relaxation cross sections to details of the interaction potentials is examined. To our knowledge, this is one of only two comparisons of ab initio quantum scattering calculations with experimental measurements of inelastic collisions at subkelvin temperatures near one Kelvin. Our work thus demonstrates the feasibility of describing cold collisions from first principles.
Angular momentum changing collisions can be suppressed in atoms whose valence electrons are submerged beneath filled shells of higher principle quantum number. To determine whether spin-exchange collisions are suppressed in these "submerged shell" atoms, we measured collisional rates for six hyperfine states of Mn at T < 1 K. Although the 3d valence electrons in Mn are submerged beneath a filled 4s orbital, we find spin-exchange rate coefficients similar to Na and H (both nonsubmerged shell atoms).