Structure and interactions of atoms and diatomic molecules: from ultracold gases to doped solids

TL;DR

The habilitation presents a two-pronged exploration of complex quantum systems: (i) precise atomic-structure calculations for lanthanide atoms and ions using a semi-empirical Racah–Slater framework (Cowan codes) supplemented by least-squares fitting (RCE, FitAik) to energies and transition probabilities, enabling accurate dynamic dipole polarizabilities and laser-cooling feasibility; and (ii) a detailed treatment of long-range interactions in ultracold systems, developed through multipolar expansions in body-fixed and space-fixed frames, with perturbation theory, symmetry considerations, and external-field couplings, applied to photoassociation, ozone-formation-like processes, and shielding of ultracold collisions. The work demonstrates extended Judd–Ofelt theory for Ln3+ dopants in solids, rigorous AC Stark-shift formulations via Floquet theory, and comprehensive LR analyses for atom–diatom and molecule–molecule scenarios, including doubly dipolar lanthanide systems. Collectively, it provides a cohesive toolkit to predict spectra, polarizabilities, and interaction energies across gaseous and solid-state environments, and to engineer control strategies such as magic trapping, optical shielding, and field-mixed dipoles for quantum technologies. The results have broad implications for ultracold chemistry, quantum simulation with strongly correlated dipolar systems, and the design of Ln-doped photonic materials and optical devices, with quantitative guidance for experiment and theory alike.

Abstract

This is the manuscript of my "Habilitation à diriger des recherches", where I present the research work that I have done after my PhD, defended in 2009. The manuscript is divided in two parts. The first one is dedicated to atomic-structure calculations with neutral and trivalent lanthanides, in the contexts of ultracold gases and rare-earth doped solids. The second part deals with long-range interactions in ultracold gases of alkali-metal atoms and diatomic molecules, as well as lanthanide atoms. The detailed description of long-range interactions serves to characterize ultralow-temperature phenomena, like photoassociation and collisional shielding.

Figures (29)

• Figure 1: Experimental energy levels of neutral erbium (Er) plotted as functions of the electronic angular momentum and sorted by parity. The arrows represent the main laser-cooling transitions with their wavelengths and linewidths.
• Figure 2: Er$^+$ : normalized level distribution as functions as the difference between calculated and experimental Landé g-factors. Levels of both parities are mixed.
• Figure 3: Er$^+$ : normalized distributions of transitions as functions of the 10-base logarithmic ratio between calculated and experimental transition probabilities.
• Figure 4: Nd : normalized distribution of levels of both parities as function of the difference between calculated and experimental Landé g-factors.
• Figure 5: Examples of polarizability uncertainties (shaded regions) for the scalar and tensor components of erbium ground (a) and 17157-cm$^{-1}$ excited levels (b). The experimental values of Ref. becher2018 are also presented with their uncertainties.