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arXiv:1310.4357 · Physical Review A

Sympathetic cooling of fluorine atoms with ultracold atomic hydrogen

Maykel Leonardo González-Martínez, Jeremy M. Hutson

Published Nov 20, 2013• 8 citations
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Abstract

We consider the prospect of using ultracold hydrogen atoms for sympathetic cooling of fluorine atoms to microkelvin temperatures. We carry out quantum-mechanical calculations on collisions between cold F and H atoms in magnetically trappable states and show that the ratio of elastic to inelastic cross sections remains high across a wide range of temperatures and magnetic fields. For F atoms initially in the spin-stretched state (${}^{2}{P}_{3/2}$, $f={m}_{f}=+2$), sympathetic cooling appears likely to succeed from starting temperatures around 1 K or even higher. This occurs because inelastic collisions are suppressed by $p$-wave and $d$-wave barriers that are 600 mK and 3.2 K high, respectively. In combination with recent results on $\mathrm{H}+\mathrm{NH}$ and $\mathrm{H}+\mathrm{OH}$ collisions [M. L. Gonz\'alez-Mart\'{\i}nez and J. M. Hutson, Phys. Rev. Lett. 111, 203004 (2013)], this establishes ultracold H atoms as a very promising and versatile coolant for atoms and molecules that cannot be laser-cooled.

DOI
10.1103/physreva.88.053420

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Acta Physica Sinica•Jan 1, 2018•0 citations
We consider the prospect of using ultracold hydrogen atoms for sympathetic cooling of fluorine atoms to microkelvin temperatures. We carry out quantum-mechanical calculations on collisions between cold F and H atoms in magnetically trappable states and show that the ratio of elastic to inelastic cross sections remains high across a wide range of temperatures and magnetic fields. For F atoms initially in the spin-stretched state (2P3/2{}^{2}{P}_{3/2}2P3/2​, f=mf=+2f={m}_{f}=+2f=mf​=+2), sympathetic cooling appears likely to succeed from starting temperatures around 1 K or even higher. This occurs because inelastic collisions are suppressed by ppp-wave and ddd-wave barriers that are 600 mK and 3.2 K high, respectively. In combination with recent results on H+NH\mathrm{H}+\mathrm{NH}H+NH and H+OH\mathrm{H}+\mathrm{OH}H+OH collisions [M. L. Gonz'alez-Mart'{\i}nez and J. M. Hutson, Phys. Rev. Lett. 111, 203004 (2013)], this establishes ultracold H atoms as a very promising and versatile coolant for atoms and molecules that cannot be laser-cooled.
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 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.
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.
Sympathetic cooling is one of the most promising techniques for producing ultracold molecules from precooled molecules. Previous researches have shown that it is inadequate to use the ultracold alkali-metal atoms as coolant for sympathetic cooling. To explore the possibility of ultracold alkali-earth-metal atoms as coolant, in this paper a theoretical investigation is performed of the cold collision dynamics for Xe-NH(X3∑-) system in magnetic fields. The interaction potential energies of Xe-NH complex are calculated respectively by using the single and double excitation coupled-cluster theory with the noniterative treatment of triple excitations[CCSD(T)] method and complete basis set limit extrapolated method. An analytic express of potential energy surface (PES) is given for the first time. A single global minimum value occurs at R=7.14a0, θ=102.76° with an energy of-153.54 cm-1, and the PES has a weak anisotropy. Combine the ab initio PES with quantum scattering theory, then the cold collisional dynamics of Xe-NH system in a magnetic field will be studied. The elastic and inelastic transition cross sections and their ratios of NH molecules in the lowest low-field following state (n=0, mj=1) under different magnetic fields and collisional energies are calculated. The results show that the elastic cross section is independent of magnetic field, and the inelastic cross section changes with magnetic field, especially at an ultracold temperature. A common rule of thumb is that to successfully implement cooling, the ratio of elastic cross section to inelastic cross section needs to reach 100 at least. The results suggest that it is likely to be a challenging work to perform sympathetic cooling of NH molecule by ultracold Xe atom.