Hybrid atom-ion systems combine the precise control of a single radio-frequency-trapped atomic ion with the rich few- to many-body phenomena of ultracold degenerate quantum gases trapped in light fields. The associated long-range interaction enables studies of impurity physics and the implementation of a single-particle quantum gas microscope, sensitive to quantities beyond the atomic density, including energy distributions, atom-atom couplings, and many-body exchange symmetry. This perspective requires atom-ion coupling, which can be tuned through resonantly enhanced scattering. While atom-ion Feshbach resonances have recently become experimentally accessible, the role of quantum statistics in resonantly enhanced three-body recombination remains largely unexplored. This thesis investigates the role of fermionic quantum statistics in atom-atom-ion three-body recombination. The experiment employs a single 138Ba+ ion immersed in an ultracold two-component Fermi gas of 6Li. An atom-ion Feshbach resonance enables resonantly enhanced recombination for one spin component, while the other component acts as a non-resonant spectating collision partner. This allows a direct comparison between recombination processes involving identical and distinguishable fermions. Experimentally, recombination rates are extracted from bath polarization-dependent ion-loss spectroscopy. Expressing the results as relative rate constants largely detaches them from the total atomic density and results in suppression of recombination in the identical fermion channel. Additional measurements of two-body reactive collisions are combined with simulations of the Fermi gas, demonstrating that density modifications arising from Fermi-Dirac statistics or mutual atom-atom attraction are insufficient to explain the observed recombination behavior. To interpret the measurements, an extension of the conventional two-step model is developed. Using a hyperspherical treatment that includes all pairwise interactions and fermionic exchange symmetry, effective relaxation rates for the loosely-bound atom-ion complex are obtained. The calculations predict a suppression of recombination involving identical fermions relative to distinguishable collision partners. The experimental observations are consistent with this prediction and provide evidence that fermionic exchange symmetry significantly affects resonantly enhanced atom-atom-ion recombination. These results establish three-body recombination as a sensitive probe of short-range quantum correlations in degenerate gases and demonstrate that a single trapped ion can be employed as a localized sensor of many-body quantum statistics.
The electronic structure of the
(LiYb)+ molecular ion is investigated with two variants of the coupled cluster method restricted to single, double, and noniterative or linear triple excitations. Potential-energy curves for the ground and excited states, permanent and transition electric dipole moments, and long-range interaction coefficients
C4 and
C6 are reported. The data are subsequently employed in scattering calculations and photoassociation studies. Feshbach resonances are shown to be measurable, despite the ion's micromotion in the Paul trap. Molecular ions can be formed in their singlet electronic ground state by one-photon photoassociation and in triplet states by two-photon photoassociation; and control of cold atom-ion chemistry based on Feshbach resonances should be feasible. Conditions for sympathetic cooling of an
Yb+ ion by an ultracold gas of Li atoms are found to be favorable in the temperature range
10nK−−10mK, and further improvements using Feshbach resonances should be possible. Overall, these results suggest excellent prospects for building a quantum simulator with ultracold
Yb+ ions and Li atoms.