Physical Review A

Zeeman relaxation of magnetically trapped Eu atoms

Yury V. Suleimanov

Published Feb 3, 2010• 10 citations

Abstract

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 ${m}_{s}=7/2$ 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 ${m}_{s}=5/2$ 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 Eu${}_{2}$.

DOI: 10.1103/physreva.81.022701

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Physical Review A

Zeeman relaxation of magnetically trapped Eu atoms

Yury V. Suleimanov

Published Feb 3, 2010• 10 citations

Publisher

Abstract

{m}_{s}=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

{m}_{s}=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 Eu

{}_{2}

DOI: 10.1103/physreva.81.022701

Related papers

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

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

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Zeeman relaxation of MnH ( X7Σ+ ) in collisions with He3 : Mechanism and comparison with experiment

Florence Turpin, Thierry Stoecklin, Philippe Halvick

We present a theoretical study of the Zeeman relaxation of the magnetically trappable lowest field seeking state of MnH (${}^{7}\ensuremath{\Sigma}$) in collisions with $^{3}\mathrm{He}$ . We analyze the collisional Zeeman transition mechanism as a function of the final diatomic state and its variation as a function of an applied magnetic field. We show that as a result of this mechanism the levels with $\ensuremath{\Delta}{M}_{j}>2$ give negligible contributions to the Zeemam relaxation cross section. We also compare our results to the experimental cross sections obtained from the buffer-gas cooling and magnetic trapping of this molecule and investigate the dependence of the Zeeman relaxation cross section on the accuracy of the three-body interaction at ultralow energies.We present a theoretical study of the Zeeman relaxation of the magnetically trappable lowest field seeking state of MnH (${}^{7}\ensuremath{\Sigma}$) in collisions with $^{3}\mathrm{He}$. We analyze the collisional Zeeman transition mechanism as a function of the final diatomic state and its variation as a function of an applied magnetic field. We show that as a result of this mechanism the levels with $\ensuremath{\Delta}{M}_{j}>2$ give negligible contributions to the Zeemam relaxation cross section. We also compare our results to the experimental cross sections obtained from the buffer-gas cooling and magnetic trapping of this molecule and investigate the dependence of the Zeeman relaxation cross section on the accuracy of the three-body interaction at ultralow energies.

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{m}_{s}=7/2

{m}_{s}=5/2

{}_{2}

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.

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.

^{14}\mathrm{N}

and

^{15}\mathrm{N}

atoms with densities $(5\ifmmode\pm\else\textpm\fi{}2)\ifmmode\times\else\texttimes\fi{}{10}^{12} {\mathrm{cm}}^{\ensuremath{-}3}$ and measure their magnetic relaxation rates at milli-Kelvin temperatures. These measurements, together with rigorous quantum scattering calculations based on accurate ab initio interaction potentials for the ${}^{7}{\ensuremath{\Sigma}}_{u}^{+}$ electronic state of

{\mathrm{N}}_{2}

demonstrate that dipolar relaxation in

\mathrm{N}+\mathrm{N}

collisions occurs at a slow rate of $~{10}^{\ensuremath{-}13} {\mathrm{cm}}^{3}$/s over a wide range of temperatures (1 mK to 1 K) and magnetic fields (10 mT to 2 T). The calculated dipolar relaxation rates are insensitive to small variations of the interaction potential and to the magnitude of the spin-exchange interaction, enabling the accurate calibration of the measured N atom density. We find consistency between the calculated and experimentally determined rates. Our results suggest that N atoms are promising candidates for future experiments on sympathetic cooling of molecules.

We present a theoretical study of the Zeeman relaxation of the magnetically trappable lowest field seeking state of MnH (${}^{7}\ensuremath{\Sigma}$) in collisions with

^{3}\mathrm{He}

. We analyze the collisional Zeeman transition mechanism as a function of the final diatomic state and its variation as a function of an applied magnetic field. We show that as a result of this mechanism the levels with $\ensuremath{\Delta}{M}_{j}>2$ give negligible contributions to the Zeemam relaxation cross section. We also compare our results to the experimental cross sections obtained from the buffer-gas cooling and magnetic trapping of this molecule and investigate the dependence of the Zeeman relaxation cross section on the accuracy of the three-body interaction at ultralow energies.