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arXiv:physics/0607084 · Physical Review Letters

Ultracold Rb-OH Collisions and Prospects for Sympathetic Cooling

Manuel Lara, John L. Bohn, Daniel Potter, Pavel Soldán, Jeremy M. Hutson

Published Nov 3, 2006• 104 citations
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Abstract

We compute ab initio cross sections for cold collisions of Rb atoms with OH radicals. We predict collision rate constants of order 10(-11) cm3/s at temperatures in the range 10-100 mK at which molecules have already been produced. However, we also find that in these collisions the molecules have a strong propensity for changing their internal state, which could make sympathetic cooling of OH in a Rb buffer gas problematic in magnetostatic or electrostatic traps.

DOI
10.1103/physrevlett.97.183201

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We compute ab initio cross sections for cold collisions of Rb atoms with OH radicals. We predict collision rate constants of order 10(-11) cm3/s at temperatures in the range 10-100 mK at which molecules have already been produced. However, we also find that in these collisions the molecules have a strong propensity for changing their internal state, which could make sympathetic cooling of OH in a Rb buffer gas problematic in magnetostatic or electrostatic traps.
We have calculated elastic and state-resolved inelastic cross sections for cold and ultracold collisions in the $\mathrm{Rb}(^{1}S)+\mathrm{O}\mathrm{H}(^{2}\ensuremath{\Pi}_{3∕2})$ system, including fine-structure and hyperfine effects. We have developed a set of five potential energy surfaces for $\mathrm{Rb}\text{\ensuremath{-}}\mathrm{O}\mathrm{H}(^{2}\ensuremath{\Pi})$ from high-level ab initio electronic structure calculations, which exhibit conical intersections between covalent and ion-pair states. The surfaces are transformed to a quasidiabatic representation. The collision problem is expanded in a set of channels suitable for handling the system in the presence of electric and/or magnetic fields, although we consider the zero-field limit in this work. Because of the large number of scattering channels involved, we propose and make use of suitable approximations. To account for the hyperfine structure of both collision partners in the short-range region we develop a frame-transformation procedure which includes most of the hyperfine Hamiltonian. Scattering cross sections on the order of ${10}^{\ensuremath{-}13}\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{2}$ are predicted for temperatures typical of Stark decelerators. We conclude that spin orientation of the partners is completely disrupted during the collision. Implications for both sympathetic cooling of OH molecules in an environment of ultracold Rb atoms and experimental observability of the collisions are discussed.
Ultracold collisions of polar OH molecules are considered in the presence of an electrostatic field. The field exerts a strong influence on both elastic and state-changing inelastic collision rate constants, leading to clear experimental signatures that should help disentangle the theory of cold molecule collisions. Based on the collision rates, we discuss the prospects for evaporative cooling of electrostatically trapped OH. We also find that the scattering properties at ultralow temperatures prove to be remarkably independent of the details of the short-range interaction, owing to avoided crossings in the long-range adiabatic potential curves. The behavior of the scattering rate constants is qualitatively understood in terms of a novel set of long-range states of the [OH]2[\mathrm{OH}{]}_{2}[OH]2​ dimer.
We report close-coupling (CC) quantum dynamics calculations for collisional excitation/de-excitation of the lowest four rotational levels of OD − and of OH − interacting with Rb atoms in a cold ion trap. The calculations are carried out over a range of energies capable of yielding the corresponding rates for state-changing events over a rather broad interval of temperatures which cover those reached in earlier cold trap experiments. They involved sympathetic cooling of the molecular anion through a cloud of laser-cooled Rb atoms, an experiment which is currently being run again through a Heidelberg–Innsbruck collaboration. The significance of isotopic effects is analysed by comparing both systems and the range of temperatures examined in the calculations is extended up to 400 K, starting from a few mK. Both cross sections and rates are found to be markedly larger than in the case of OD − /OH − interacting the He atoms under the same conditions, and the isotopic effects are also seen to be rather significant at the energies examined in the present study. Such findings are discussed in the light of the observed trap losses of molecular anions.
We show theoretically that ultracold hydrogen atoms have very favorable properties for sympathetic cooling of molecules to microkelvin temperatures. We calculate the potential energy surfaces for spin-polarized interactions of H atoms with the prototype molecules $\mathrm{NH}(^{3}\ensuremath{\Sigma}^{\ensuremath{-}})$ and $\mathrm{OH}(^{2}\ensuremath{\Pi})$ and show that they are shallow (50 to $80\text{ }\text{ }{\mathrm{cm}}^{\ensuremath{-}1}$) and only weakly anisotropic. We carry out quantum collision calculations on H+NH\mathrm{H}+\mathrm{NH}H+NH and H+OH\mathrm{H}+\mathrm{OH}H+OH and show that the ratio of elastic to inelastic cross sections is high enough to allow sympathetic cooling from temperatures well over 1 K for NH and around 250 mK for OH.
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.
We model sympathetic cooling of ground-state CaF molecules by ultracold Li and Rb atoms. The molecules are moving in a microwave trap, while the atoms are trapped magnetically. We calculate the differential elastic cross sections for CaF-Li and CaF-Rb collisions, using model Lennard-Jones potentials adjusted to give typical values for the sss-wave scattering length. Together with trajectory calculations, these differential cross sections are used to simulate the cooling of the molecules, the heating of the atoms, and the loss of atoms from the trap. We show that a hard-sphere collision model based on an energy-dependent momentum transport cross section accurately predicts the molecule cooling rate but underestimates the rates of atom heating and loss. Our simulations suggest that Rb is a more effective coolant than Li for ground-state molecules, and that the cooling dynamics is less sensitive to the exact value of the sss-wave scattering length when Rb is used. Using realistic experimental parameters, we find that molecules can be sympathetically cooled to $100\phantom{\rule{0.28em}{0ex}}\ensuremath{\mu}\mathrm{K}$ in about 10 s. By applying evaporative cooling to the atoms, the cooling rate can be increased and the final temperature of the molecules can be reduced to $1 \ensuremath{\mu}\mathrm{K}$ within 30 s.