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arXiv:1508.03987 · Physical Review A

Modeling sympathetic cooling of molecules by ultracold atoms

Jongseok Lim, Matthew D. Frye, Jeremy M. Hutson, Michael R. Tarbutt

Published Nov 13, 2015• 55 citations
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Abstract

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 $s$-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 $s$-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.

DOI
10.1103/physreva.92.053419

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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\ensuremathμK100\phantom{\rule{0.28em}{0ex}}\ensuremath{\mu}\mathrm{K}100\ensuremathμK 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\ensuremathμK1 \ensuremath{\mu}\mathrm{K}1\ensuremathμK within 30 s.
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.
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