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.

Defects in thermosensitive colloidal crystals

Poly-N-Isopropylacrylamide (PNIPAM) colloidal particles form crystal phases that show a thermosensitive behaviour and can be used as atomic model systems. This polymer has both hydrophilic and hydrophobic character and has interesting stimuli-responsive properties in aqueous solution, of which the most important is the temperature response. Above a certain temperature, called Lower Critical Solution Temperature (LCST), the system undergoes a volume phase transition (VPT). Above the LCST, the water is expelled from the polymer network and the swollen state at low temperature transforms into a shrunken state at high temperature. The thermoresponsive behaviour of PNIPAM can be influenced by pH and ionic strength, as well as by the presence of copolymers, such as acrylic acid. In a system formed both by particles of PNIPAM and PNIPAM doped with acrylic acid, one can control the size ratio of the two components by changing the temperature of the mixture, while keeping particle interactions relatively the same. It is therefore possible to obtain thermoresponsive colloidal crystal in which temperature changes induce defects whose formation processes and dynamics can be analysed in an optical microscope at a convenient spatial and temporal scale. The goal of this thesis project was to find the conditions in which such a system could be formed, by using characterization techniques such as Static Light Scattering, Dynamic Light Scattering and Confocal Laser Scanning Microscopy. Two PNIPAM-AAc systems were available, and after characterization it was possible to select a suitable one, on the basis of its low polydispersity and the lack of a VPT, regardless of the external conditions (system JPN_7). The synthesis of a PNIPAM system was attempted, with particles of dimensions matching the JPN_7 system and, unlike JPN_7, displaying a VPT, and one suitable candidate for the mixed system was finally found (system CB_5). The best conditions to obtain thermoresponsive crystal were selected, and the formation and healing of defects were investigated with CLSM temperature scans. The obtained results show that the approach is the correct one and that the present report could represent a useful start for future developments in defect analysis and defect dynamics studies.