Physical Review A

Zeeman relaxation induced by spin-orbit coupling in cold antimony-helium collisions

Colin B. Connolly, Yat Shan Au, Eunmi Chae, Timur V. Tscherbul, Alexei A. Buchachenko, Wolfgang Ketterle, John M. Doyle

Published Jul 15, 2013• 3 citations

Abstract

We investigate Zeeman relaxation in cold Sb(${}^{4}{S}_{3/2}^{\ensuremath{\circ}}$)--He collisions in a magnetic field. Ensembles of $>$${10}^{13}$ laser-ablated Sb atoms are cooled in cryogenic ${}^{4}$He buffer gas to 800 mK and inelastic collisions are observed to equilibrate the ${m}_{J}$-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--${}^{4}$He 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}$10$%$ 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.

DOI: 10.1103/physreva.88.012707

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Physical Review A

Zeeman relaxation induced by spin-orbit coupling in cold antimony-helium collisions

Colin B. Connolly, Yat Shan Au, Eunmi Chae, Timur V. Tscherbul, Alexei A. Buchachenko, Wolfgang Ketterle, John M. Doyle

Published Jul 15, 2013• 3 citations

Publisher

Abstract

We investigate Zeeman relaxation in cold Sb(

{}^{4}{S}_{3/2}^{\ensuremath{\circ}}

)--He collisions in a magnetic field. Ensembles of

>$${10}^{13}

laser-ablated Sb atoms are cooled in cryogenic

{}^{4}

He buffer gas to 800 mK and inelastic collisions are observed to equilibrate the

{m}_{J}

-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}

He 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}

%

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.

DOI: 10.1103/physreva.88.012707

Related papers

Spin-orbit interaction and large inelastic rates in bismuth-helium collisions

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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.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.

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We present a combined experimental and theoretical study of angular momentum depolarization in cold collisions of $^{2}P$ atoms in the presence of an external magnetic field. We show that collision-induced Zeeman relaxation of $\text{Ga}({^{2}P}_{1/2})$ and $\text{In}({^{2}P}_{1/2})$ atoms in cold $^{4}\text{H}\text{e}$ gas is dramatically suppressed compared to atoms in ${^{2}P}_{3/2}$ states. Using rigorous quantum-scattering calculations based on ab initio interaction potentials, we demonstrate that Zeeman transitions in collisions of atoms in ${^{2}P}_{1/2}$ electronic states occur via couplings to the ${^{2}P}_{3/2}$ state induced by the anisotropy of the interaction potential. Our results suggest the feasibility of sympathetic cooling and magnetic trapping of ${^{2}P}_{1/2}$ -state atoms, such as halogens, thereby opening up exciting areas of research in precision spectroscopy and cold-controlled chemistry.We present a combined experimental and theoretical study of angular momentum depolarization in cold collisions of $^{2}P$ atoms in the presence of an external magnetic field. We show that collision-induced Zeeman relaxation of $\text{Ga}({^{2}P}_{1/2})$ and $\text{In}({^{2}P}_{1/2})$ atoms in cold $^{4}\text{H}\text{e}$ gas is dramatically suppressed compared to atoms in ${^{2}P}_{3/2}$ states. Using rigorous quantum-scattering calculations based on ab initio interaction potentials, we demonstrate that Zeeman transitions in collisions of atoms in ${^{2}P}_{1/2}$ electronic states occur via couplings to the ${^{2}P}_{3/2}$ state induced by the anisotropy of the interaction potential. Our results suggest the feasibility of sympathetic cooling and magnetic trapping of ${^{2}P}_{1/2}$-state atoms, such as halogens, thereby opening up exciting areas of research in precision spectroscopy and cold-controlled chemistry.

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

Colin B. Connolly

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.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.

Nov 15, 20122 citations

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

Alexei A. Buchachenko, Grzegorz Chałasiński, Małgorzata M. Szczęśniak +1 more

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.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.

Physical Review AAug 2, 200615 citations

We investigate Zeeman relaxation in cold Sb(

{}^{4}{S}_{3/2}^{\ensuremath{\circ}}

)--He collisions in a magnetic field. Ensembles of

>$${10}^{13}

laser-ablated Sb atoms are cooled in cryogenic

{}^{4}

He buffer gas to 800 mK and inelastic collisions are observed to equilibrate the

{m}_{J}

-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}

\ensuremath{\approx}

%

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.

We present a combined experimental and theoretical study of angular momentum depolarization in cold collisions of

^{2}P

atoms in the presence of an external magnetic field. We show that collision-induced Zeeman relaxation of

\text{Ga}({^{2}P}_{1/2})

and

\text{In}({^{2}P}_{1/2})

atoms in cold

^{4}\text{H}\text{e}

gas is dramatically suppressed compared to atoms in

{^{2}P}_{3/2}

states. Using rigorous quantum-scattering calculations based on ab initio interaction potentials, we demonstrate that Zeeman transitions in collisions of atoms in

{^{2}P}_{1/2}

electronic states occur via couplings to the

{^{2}P}_{3/2}

state induced by the anisotropy of the interaction potential. Our results suggest the feasibility of sympathetic cooling and magnetic trapping of

{^{2}P}_{1/2}

-state atoms, such as halogens, thereby opening up exciting areas of research in precision spectroscopy and cold-controlled chemistry.

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.