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Physical Review Letters

Zeeman Relaxation of CaF in Low-Temperature Collisions with Helium

Kenneth Maussang, Dima Egorov, Joel S. Helton, Scott V. Nguyen, John M. Doyle

Published Mar 29, 2005• 77 citations
Publisher

Abstract

The collision-induced Zeeman relaxation rate for collisions of CaF ${X}^{2}\ensuremath{\Sigma}({v}^{\ensuremath{'}\ensuremath{'}}=0)$ with $^{3}\mathrm{He}$ is measured to be ${\ensuremath{\Gamma}}_{\mathrm{Z}}=(7.7+5.4/\ensuremath{-}2.5)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}15}\text{ }{\mathrm{cm}}^{3}/\mathrm{s}$ at 2 K. This rate is a direct measurement of the influence of spin-rotation coupling on Zeeman relaxation in the first rotational level of CaF. The relationship of this rate to known molecular constants is consistent with recent theory of cold molecular collisions and outlines the $^{2}\ensuremath{\Sigma}$ molecules conducive to magnetic trapping.

DOI
10.1103/physrevlett.94.123002

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The collision-induced Zeeman relaxation rate for collisions of CaF X2\ensuremathΣ(v\ensuremath′\ensuremath′=0){X}^{2}\ensuremath{\Sigma}({v}^{\ensuremath{'}\ensuremath{'}}=0)X2\ensuremathΣ(v\ensuremath′\ensuremath′=0) with 3He^{3}\mathrm{He}3He is measured to be \ensuremathΓZ=(7.7+5.4/\ensuremath−2.5)\ifmmode×\else\texttimes\fi10\ensuremath−15 cm3/s{\ensuremath{\Gamma}}_{\mathrm{Z}}=(7.7+5.4/\ensuremath{-}2.5)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}15}\text{ }{\mathrm{cm}}^{3}/\mathrm{s}\ensuremathΓZ​=(7.7+5.4/\ensuremath−2.5)\ifmmode×\else\texttimes\fi10\ensuremath−15 cm3/s at 2 K. This rate is a direct measurement of the influence of spin-rotation coupling on Zeeman relaxation in the first rotational level of CaF. The relationship of this rate to known molecular constants is consistent with recent theory of cold molecular collisions and outlines the 2\ensuremathΣ^{2}\ensuremath{\Sigma}2\ensuremathΣ molecules conducive to magnetic trapping.
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 measure and theoretically determine the effect of molecular rotational splitting on Zeeman relaxation rates in collisions of cold 3Sigma molecules with helium atoms in a magnetic field. All four stable isotopomers of the imidogen (NH) molecule are magnetically trapped and studied in collisions with 3He and 4He. The 4He data support the predicted 1/B_{e};{2} dependence of the collision-induced Zeeman relaxation rate coefficient on the molecular rotational constant B_{e}. The measured 3He rate coefficients are much larger than the 4He coefficients, depend less strongly on B_{e}, and theoretical analysis indicates they are strongly affected by a shape resonance. The results demonstrate the influence of molecular structure on collisional energy transfer at low temperatures.
The Zeeman effect in the excited A 2Pi(3/2) state of CaF is measured and analyzed over a wide range of magnetic fields. It is found that the splitting of the Zeeman levels is largely determined by the coupling between different rotational states and there are no low-field seeking states in the J=3/2 manifold of Zeeman levels at high magnetic fields. A model of the Zeeman spectrum based on the ligand-field theory of CaF is shown to be accurate in the interval of magnetic fields 0-5 Tesla. This demonstrates that the magnetic moment of the CaF(A 2Pi(3/2)) molecule is effectively determined by the spin angular momentum of a single electron and the orbital motion of the valence electron around the Ca2+ core. An analysis of the Zeeman spectrum as a function of the molecular rotational constant indicates that 2Pi(3/2) molecules should have significant rotational constants (at least as large as twice the rotational constant of CaF) to be amenable to magnetic trapping in high fields.
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.
We prepare mixtures of ultracold CaF molecules and Rb atoms in a magnetic trap and study their inelastic collisions. When the atoms are prepared in the spin-stretched state and the molecules in the spin-stretched component of the first rotationally excited state, they collide inelastically with a rate coefficient k_{2}=(6.6±1.5)×10^{-11} cm^{3}/s at temperatures near 100 μK. We attribute this to rotation-changing collisions. When the molecules are in the ground rotational state we see no inelastic loss and set an upper bound on the spin-relaxation rate coefficient of k_{2}<5.8×10^{-12} cm^{3}/s with 95% confidence. We compare these measurements to the results of a single-channel loss model based on quantum defect theory. The comparison suggests a short-range loss parameter close to unity for rotationally excited molecules, but below 0.04 for molecules in the rotational ground state.
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.