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Physical Review A

Ab initiostudy of Tm-He interactions and dynamics in a magnetic trap

Alexei A. Buchachenko, Grzegorz Chałasiński, Małgorzata M. Szczęśniak, Roman V. Krems

Published Aug 2, 2006• 15 citations
Publisher

Abstract

The dynamics of magnetic relaxation of Tm atoms in cold helium gas is investigated using ab initio interaction potentials between $\mathrm{Tm}(^{2}F)$ and He atoms. The interaction of $\mathrm{Tm}(^{2}F)$ 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 $R=5.4\phantom{\rule{0.3em}{0ex}}\mathrm{\AA{}}$. 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 $\mathrm{Tm}(^{2}F_{7∕2})$ atoms in the maximally stretched $M=7∕2$ sublevel at the temperature $0.8\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, 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.

DOI
10.1103/physreva.74.022705

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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 \ensuremathΣ+{\ensuremath{\Sigma}}^{+}\ensuremathΣ+, \ensuremathΠ\ensuremath{\Pi}\ensuremathΠ, \ensuremathΔ\ensuremath{\Delta}\ensuremathΔ, and \ensuremathΦ\ensuremath{\Phi}\ensuremathΦ symmetries, which are found to be degenerate to within 0.1cm\ensuremath−10.1\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}0.1cm\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×\else\texttimes\fi10\ensuremath−15cm3s\ensuremath−11.5\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}1.5\ifmmode×\else\texttimes\fi10\ensuremath−15cm3s\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±\else\textpm\fi2.1)\ifmmode×\else\texttimes\fi10\ensuremath−15cm3s\ensuremath−1(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}(5.0\ifmmode±\else\textpm\fi2.1)\ifmmode×\else\texttimes\fi10\ensuremath−15cm3s\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.
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.
Ab initio calculations of cross sections and rate constants for elastic scattering and Zeeman relaxation in collisions of $\mathrm{NH}(X{}^{3}{\ensuremath{\Sigma}}^{\ensuremath{-}})$ molecules with 3He{}^{3}\mathrm{He}3He atoms in a magnetic field are presented and the mechanism for Zeeman transitions in ground-state ${}^{3}\ensuremath{\Sigma}$ molecules is established. The potential surface for He-NH interaction is obtained using all-electron coupled-cluster calculations with single, double, and noniterative triple excitations in a basis set augmented by bond functions. The ratio of the rates for elastic energy transfer and Zeeman relaxation in NH-3He{}^{3}\mathrm{He}3He collisions exceeds 105{10}^{5}105 at temperatures between 0.50.50.5 and 1 K.
NH radicals are magnetically trapped and their Zeeman relaxation and energy transport collision cross sections with helium are measured. Continuous buffer-gas loading of the trap is direct from a room-temperature molecular beam. The Zeeman relaxation (inelastic) cross section of magnetically trapped electronic, vibrational, and rotational ground state NH molecules in collisions with 3He^{3}\mathrm{He}3He is measured to be $3.8\ifmmode\pm\else\textpm\fi{}1.1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}19}\text{ }\text{ }{\mathrm{cm}}^{2}$ at 710 mK. The NH-He energy transport cross section is also measured, indicating a ratio of diffusive to inelastic cross sections of $\ensuremath{\gamma}=7\ifmmode\times\else\texttimes\fi{}{10}^{4}$, in agreement with recent theory [R. V. Krems, H. R. Sadeghpour, A. Dalgarno, D. Zgid, J. K\l{}os, and G. Cha\l{}asi\ifmmode \acute{n}\else \'{n}\fi{}ski, Phys. Rev. A 68, 051401 (2003)].
We present an experimental and theoretical study of atom-molecule collisions in a mixture of cold, trapped N atoms and NH molecules at a temperature of $\ensuremath{\sim}600\text{ }\text{ }\mathrm{mK}$. We measure a small N+NH\mathrm{N}+\mathrm{NH}N+NH trap loss rate coefficient of ${k}_{\mathrm{loss}}^{(\mathrm{N}+\mathrm{NH})}=9(5)(3)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}13}\text{ }\text{ }{\mathrm{cm}}^{3}\text{ }{\mathrm{s}}^{\ensuremath{-}1}$. Accurate quantum scattering calculations based on ab initio interaction potentials are in agreement with experiment and indicate the magnetic dipole interaction to be the dominant loss mechanism. Our theory further indicates the ratio of N+NH\mathrm{N}+\mathrm{NH}N+NH elastic-to-inelastic collisions remains large (>100>100>100) into the mK regime.
Current research in magnetic trapping of the metal atoms is commented upon from the viewpoint of the theory of interatomic interactions and collision dynamics at sub-kelvin temperatures. Atom–atom interactions that lead to collision-induced transitions between different Zeeman states of complex atoms are discussed using the concept of interaction anisotropy. Theoretical results for Zeeman relaxation dynamics for lanthanides, transition and heavy main group metals are reviewed and compared with recent experimental findings. Possible directions of future research are outlined.
We perform rigorous quantum mechanical calculations for collisions between magnetically trapped Eu atoms to elucidate the results of recent experimental studies. We show that the relaxation from the maximally stretched ms=7/2{m}_{s}=7/2ms​=7/2 level is entirely determined by the magnetic dipole-dipole interaction and analyze the role of the electronic spin-exchange interaction in transitions from the lower-energy Zeeman levels. The relaxation of the ms=5/2{m}_{s}=5/2ms​=5/2 state is shown to be very sensitive to the spin-exchange parameter that determines the splitting between the lowest electronic states of the Eu dimer. We suggest that cold collision experiments with trapped atoms can be used as a tool for obtaining accurate information on the electronic spin anisotropy in complex molecules such as Eu2{}_{2}2​.