Preparation of ground state Ultracold Lithium Dimers and Coherent Control of Their Reactions: A Theoretical Study

Abstract

This thesis develops the prerequisites for coherent control of the ultracold isotope-exchange reaction ${}^{6}\mathrm{Li}{}^{7}\mathrm{Li}+{}^{6}\mathrm{Li}{}^{7}\mathrm{Li} \rightarrow {}^{6}\mathrm{Li}_{2}+{}^{7}\mathrm{Li}_{2}$, a versatile platform for studying and controlling state-to-state reaction dynamics. First, we develop methods to prepare lithium molecules in rovibrational ground states through coherent assembly: free ultracold atoms are magneto-associated into weakly bound Feshbach molecules and then transferred to deeply bound ground states using species-dependent STIRAP. To enable this, we characterize the near-threshold scattering properties of $^{6}$Li$_2$, $^{7}$Li$_2$, and $^{6}$Li$^{7}$Li using coupled-channel calculations with optimized Morse/Long-Range potentials fit to threshold data. These refined potentials provide the full characterization of the Feshbach resonances relevant to molecule formation. From calculated transition dipole matrix elements, determined by vibrational overlaps (Franck-Condon factors) and spin character, we identify candidate pump and Stokes transitions and the conditions for efficient STIRAP transfer. Second, we develop a scheme for coherent control of ultracold collisions based on identical-particle symmetry, in which the reactants are prepared in coherent superpositions. Using $\mathrm{Li} + \mathrm{Li}$ as a model system, we show that exchange symmetry enables symmetry-protected control of the total scattering cross section. This mechanism can be directly generalized to $^{6}$Li$^{7}$Li +$^{6}$Li$^{7}$Li collisions, indicating that full control of collisions between identical fermionic molecules is achievable. These results guide the experimental preparation of ultracold lithium molecules and establish this reaction as a promising platform for coherent control in ultracold chemistry.