Theory of Hyperfine Effects in Interacting Atoms.

S. Dangel, R. Holzner

The conventional $J=1/2\ensuremath{\leftrightarrow}J=1/2$ model is successful for the qualitative description of the interaction of sodium atoms and laser light tuned close to the atomic ${D}_{1}$ transition. However, time constants for dynamic effects due to optical pumping predicted by the model are about an order of magnitude too short compared to experimental observations. The inclusion of hyperfine states in the quantum-mechanical description of the atom leads to a satisfactory model that also predicts the correct absorption due to atomic diffusion and allows for the description of effects related to population trapping. This hyperfine model is derived in detail and compared with the $J=1/2\ensuremath{\leftrightarrow}J=1/2$ approximation.

Supriya Ray

Ronald A. Lovett

Ming Li, Li You, Bo Gao

A quantum theory of ion-atom interaction that is applicable at energies comparable to or smaller than the atomic hyperfine splitting and that takes proper account of the effects of identical nuclei is presented, revealing the subtlety and the complexity of cold ion-atom interactions.

Chizuko M. Dutta

Denis Janković

This thesis integrates quantum computing, optimal control theory, nuclear structure, hyperfine interactions, f-elements, crystal field theory, and molecular magnetism, focusing on lanthanide-organic complexes, particularly TbPc\textsubscript{2}, as potential molecular quantum processors. The research begins with a theoretical overview, highlighting the convergence of these fields and the role of lanthanide chemistry. Key properties of lanthanides are analyzed, including their atomic and ionic states, ligand field interactions, and responses to external fields. Detailed discussions cover non-interacting electrons, Coulomb repulsion, spin-orbit coupling, and hyperfine coupling, as well as the transition from crystal field theory to ligand field theory and the capabilities of ligand field DFT. The hyperfine interaction is examined through the Dirac equation, incorporating relativity into the Schrödinger equation. Topics include mass corrections, muonic atoms, and hyperfine constants. Quantum computing with nuclear spins in lanthanides is explored, introducing qubits, qudits, quantum gates, algorithms, and relevant timescales. Optimal gate generation is investigated, aiming to develop efficient qudit gates, with TbPc\textsubscript{2} as a practical example. The Prouhet-Thue-Morse sequence is analyzed for its properties and applications in quantum computing. The thesis concludes with future research directions, including decoherence studies, effects of ligand composition, hyperfine constant calculations, and qudit gate optimization