Sympathetic cooling of the Ba$^+$ ion by collisions with ultracold Rb atoms: theoretical prospects

TL;DR

This paper uses advanced quantum chemistry methods to compute interaction potentials and collision cross sections for Ba$^+$ ions and ultracold Rb atoms, indicating the feasibility of sympathetic cooling.

Contribution

It provides detailed ab initio potential energy curves, coupling matrix elements, and scattering calculations for the Ba$^+$-Rb system, advancing the theoretical understanding of ion-atom interactions.

Findings

Inelastic charge transfer cross section is much smaller than elastic cross section up to 1 mK.

Relativistic and nonrelativistic potentials yield consistent scattering results.

Results support the possibility of sympathetic cooling of Ba$^+$ ions with ultracold Rb atoms.

Abstract

State-of-the-art {\em ab initio} techniques have been applied to compute the potential energy curves of the (BaRb)$^+$ molecular ion in the Born-Oppenheimer approximation. The long-range coefficients describing the electrostatic, induction, and dispersion interactions at large interatomic distances are also reported. The electric transition dipole moments governing the X$^1\Sigma \to ^1\Sigma, ^1\Pi$ have been obtained as the first residue of the polarization propagator computed with the linear response coupled-cluster method restricted to single and double excitations. Nonadiabatic radial and angular coupling matrix elements, as well as the spin-orbit coupling matrix elements have been evaluated using the multireference configuration interaction method restricted to single and double excitations with a large active space. With these couplings, the spin-orbit coupled (relativistic) potential energy curves for the 0$^+$ and 1 states relevant for the running experiments have been obtained. Finally, relativistic transition moments and nonadiabatic coupling matrix elements were obtained from the nonrelativistic results and spin-orbit eigenvectors. The electronic structure input has been employed in the single channel scattering calculations of the collisional cross sections between the Ba$^+$ ion and Rb atom. Both nonrelativistic and relativistic potentials were used in these calculations. Our results show that the inelastic cross section corresponding to the charge transfer from the Rb atom to the Ba$^+$ ion is much smaller than the elastic one over a wide range of energies up to 1 mK. This suggests that sympathetic cooling of the Ba$^+$ ion by collisions with ultracold Rb atoms should be possible.