Ultracold Bose-Fermi mixtures with pairing: quantum phase transition, mechanical stability, and trap confinement

Ultracold dilute gases occupy an important role in modern physics and they are employed to verify fundamental quantum theories in most branches of theoretical physics. The scope of this thesis work is the study of Bose-Fermi (BF) mixtures at zero temperature with a tunable pairing between bosons and fermions. The mixtures are treated with diagrammatic quantum many-body methods based on the so-called T-matrix formalism. Starting from the Fermi-polaron limit, I will explore various values of relative concentrations up to mixtures with a majority of bosons, a case barely considered in previous works. An unexpected quantum phase transition is found to occur in a certain range of BF coupling for mixture with a slight majority of bosons. The mechanical stability of mixtures has been analysed, when the boson-fermion interaction is changed from weak to strong values, in the light of experimental results recently obtained for a double-degenerate Bose-Fermi mixture of 23 Na - 40 K. A possible improvement in the description of the boson-boson repulsion based on Popov's theory is proposed. Finally, the effects of a harmonic trapping potential are described, with a comparison with the experimental data for the condensate fraction recently obtained for a trapped 23 Na - 40 K mixture.

Study of the activity and enantioselectivity of alginate-based catalysts in Friedel-Crafts reactions

This thesis is part of a long-term project which aims to demonstrate for the first time that alginate gel beads can be used as chiral heterogeneous catalysts for enantioselective reactions. Alginate barium beads were prepared as previously optimized and applied to the Friedel-Crafts reaction between indoles and nitroalkenes. New substrates were tested, showing that the reaction can accommodate different nitroalkenes and indoles, affording the corresponding products with moderate yields and good enantioselectivities. However, aliphatic nitroalkenes cannot be used as they degrade under the catalytic reaction conditions. Preliminary study on the recyclability of the heterogeneous catalyst indicated a moderate stability of the catalyst, which can be used for few cycles with a slight erosion of enantioinducing power. Some directions for future improvements (storage and work-up solvent, use of ultrasonic bath) have been suggested.