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arXiv:1010.2567 · Physical Review Letters

Sympathetic Cooling of Polyatomic Molecules with S -State Atoms in a Magnetic Trap

Timur V. Tscherbul, Hua‐Gen Yu, A. Dalgarno

Published Feb 18, 2011• 34 citations
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Abstract

We present a rigorous theoretical study of low-temperature collisions of polyatomic molecular radicals with (1)S(0) atoms in the presence of an external magnetic field. Accurate quantum scattering calculations based on ab initio and scaled interaction potentials show that collision-induced spin relaxation of the prototypical organic molecule CH(2)(X(3)B(1)) (methylene) and nine other triatomic radicals in cold (3)He gas occurs at a slow rate, demonstrating that cryogenic buffer-gas cooling and magnetic trapping of these molecules is feasible with current technology. Our calculations further suggest that it may be possible to create ultracold gases of polyatomic molecules by sympathetic cooling with alkaline-earth atoms in a magnetic trap.

DOI
10.1103/physrevlett.106.073201

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We present a rigorous theoretical study of low-temperature collisions of polyatomic molecular radicals with (1)S(0) atoms in the presence of an external magnetic field. Accurate quantum scattering calculations based on ab initio and scaled interaction potentials show that collision-induced spin relaxation of the prototypical organic molecule CH(2)(X(3)B(1)) (methylene) and nine other triatomic radicals in cold (3)He gas occurs at a slow rate, demonstrating that cryogenic buffer-gas cooling and magnetic trapping of these molecules is feasible with current technology. Our calculations further suggest that it may be possible to create ultracold gases of polyatomic molecules by sympathetic cooling with alkaline-earth atoms in a magnetic trap.
Cold collisions of polyatomic molecular radicals with S-state atoms in a magnetic field: An ab initio study of He + CH2(X~){\rm CH}_2(\tilde{X})CH2​(X~) CH 2(X) collisions
We develop a rigorous quantum mechanical theory for collisions of polyatomic molecular radicals with S-state atoms in the presence of an external magnetic field. The theory is based on a fully uncoupled space-fixed basis set representation of the multichannel scattering wave function. Explicit expressions are presented for the matrix elements of the scattering Hamiltonian for spin-1/2 and spin-1 polyatomic molecular radicals interacting with structureless targets. The theory is applied to calculate the cross sections and thermal rate constants for spin relaxation in low-temperature collisions of the prototypical organic molecule methylene [CH(2)(X(3)B(1))] with He atoms. To this end, two accurate three-dimensional potential energy surfaces (PESs) of the He-CH(2)(X(3)B(1)) complex are developed using the state-of-the-art coupled-cluster method including single and double excitations along with a perturbative correction for triple excitations and large basis sets. Both PESs exhibit shallow minima and are weakly anisotropic. Our calculations show that spin relaxation in collisions of CH(2), CHD, and CD(2) molecules with He atoms occurs at a much slower rate than elastic scattering over a large range of temperatures (1 μK-1 K) and magnetic fields (0.01-1 T), suggesting excellent prospects for cryogenic helium buffer-gas cooling of ground-state ortho-CH(2)(X(3)B(1)) molecules in a magnetic trap. Furthermore, we find that ortho-CH(2) undergoes collision-induced spin relaxation much more slowly than para-CH(2), which indicates that magnetic trapping can be used to separate nuclear spin isomers of open-shell polyatomic molecules.
We explore the suitability of ultracold collisions between spin-polarized $\mathrm{SrF}(^{2}\mathrm{\ensuremath{\Sigma}}^{+})$ molecules and Rb(2S)\mathrm{Rb}(^{2}S)Rb(2S) atoms as elementary steps for the sympathetic cooling of $\mathrm{SrF}(^{2}\mathrm{\ensuremath{\Sigma}}^{+})$ molecules in a magnetic trap. To this end, we carry out quantum-mechanical scattering calculations on ultracold Rb + SrF collisions in a magnetic field based on an accurate potential-energy surface for the triplet electronic state of Rb-SrF developed ab initio using a spin-restricted coupled cluster method with single, double, and noniterative triple excitations [RCCSD(T)]. The Rb-SrF interaction has a global minimum with a well depth of 3444 ${\mathrm{cm}}^{\ensuremath{-}1}$ in a bent geometry and a shallow local minimum in the linear geometry. Despite such a strong and anisotropic interaction, we find that converged close-coupling scattering calculations on Rb + SrF collisions in a magnetic field are still possible using rotational basis sets including up to 125 closed rotational channels in the total angular momentum representation. Our calculations show that electronic spin relaxation in fully spin-polarized Rb-SrF collisions occurs much more slowly than elastic scattering over a wide range of magnetic fields (1--1000 G) and collision energies (${10}^{\ensuremath{-}5}--{10}^{\ensuremath{-}3}$ K), suggesting good prospects of sympathetic cooling into the microkelvin regime of laser-cooled $\mathrm{SrF}(^{2}\mathrm{\ensuremath{\Sigma}}^{+})$ molecules with spin-polarized Rb(2S)\mathrm{Rb}(^{2}S)Rb(2S) atoms in a magnetic trap. We show that incoming ppp-wave scattering plays a significant role in ultracold collisions due to the large reduced mass of the Rb-SrF collision pair. The calculated magnetic-field dependence of the inelastic cross sections at $1.4\phantom{\rule{0.28em}{0ex}}\ensuremath{\mu}\mathrm{K}$ displays a rich resonance structure including a low-field ppp-wave resonance, which suggests that external magnetic fields can be used to enhance the efficiency of sympathetic cooling in heavy atom-molecule mixtures.
We report a combined experimental and theoretical study of collision-induced dipolar relaxation in a cold spin-polarized gas of atomic nitrogen (N). We use buffer gas cooling to create trapped samples of 14N^{14}\mathrm{N}14N and 15N^{15}\mathrm{N}15N 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 N2{\mathrm{N}}_{2}N2​ demonstrate that dipolar relaxation in N+N\mathrm{N}+\mathrm{N}N+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.
The prospects of sympathetic cooling of polar molecules with magnetically cotrapped alkali-metal atoms are generally considered poor due to strongly anisotropic atom-molecule interactions leading to large spin relaxation rates. Using rigorous quantum scattering calculations based on ab initio interaction potentials, we show that inelastic spin relaxation in low-temperature collisions of CaH(${}^{2}\ensuremath{\Sigma}$) molecules with Li and Mg atoms occurs at a slow rate despite the strongly anisotropic interactions. This unexpected result, which we rationalize using multichannel quantum-defect theory, opens up the possibility of sympathetic cooling of polar ${}^{2}\ensuremath{\Sigma}$ molecules with alkali-metal atoms in a magnetic trap and with alkaline-earth-metal atoms in an optical dipole trap.
We have demonstrated that a supersonic beam of methyl radicals (CH_{3}) in the ground rotational state of both para and ortho species has been slowed down to standstill with a magnetic molecular decelerator, and successfully captured spatially in an anti-Helmholtz magnetic trap for >1 s. The trapped CH_{3} radicals have a mean translational temperature of about 200 mK with an estimated density of >5.0×10^{7} cm^{-3}. The methyl radical is an ideal system for the study of cold molecules not only because of its high reactivities at low temperatures, but also because further cooling below 1 mK is plausible via sympathetic cooling with ultracold atoms. The demonstrated trapping capability of methyl radicals opens up various possibilities for realizing ultracold ensembles of molecules towards Bose-Einstein condensation of polyatomic molecules and investigations of reactions governed by quantum statistics.