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 are 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$\mu$K in about 10s. 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$\mu$K within 30s.
Highlights
Ultracold molecules are important for several applications in physics and chemistry
We model sympathetic cooling of ground-state CaF molecules by ultracold Li and Rb atoms
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
Summary
Ultracold molecules are important for several applications in physics and chemistry. Cold molecules have already been used to test theories that extend the standard model of particle physics, for example, by measuring the electron’s electric dipole moment [1,2] or searching for changes in the fundamental constants [3,4]. We introduce a new collision model that takes account of the full energy dependence of the differential cross sections We show that this model produces significantly slower sympathetic cooling in the early stages than the original hard-sphere model. We consider approximations to the full model and show that a model that uses hard-sphere scattering based on the energy-dependent transport cross section ση(1) [34] produces accurate results for the cooling of the molecules but not for heating and loss of the coolant atoms. Because the cross section is very sensitive to the exact form of the atom-molecule interaction potential, especially at low energies, we study sympathetic cooling for a range of typical values of the s-wave scattering length. We investigate how evaporative cooling of the atoms can be used to speed up the sympathetic cooling rate and lower the final temperature obtained
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