Final Report Summary - QGBE (Quantum Gases Beyond Equilibrium) The QGBE (Quantum Gases Beyond Equilibrium) project has concerned the theoretical investigation of the non equilibrium behavior of ultracold gases in various conditions of trapping, temperature and interactions. The research work has been carried out according to the initial plans and strategies. A large number (94) of scientific papers has been published, most of them on outstanding scientific journals (18 articles in Physical Review Letters, 47 articles in Physical Review, 1 article in Nature, 1 article in Nature Photonics, and 6 articles in New Journal of Physics), revealing the richness of the directions of theoretical research pursued within the project. THERMODYNAMICS AND TRANSPORT PHENOMENA. We have carried out a systematic study of the dynamic behavior of Fermi superfluids at finite temperature. The investigation of second sound, carried out in collaboration with the Innsbruck team headed by R. Grimm, was one of the key scientific output of this actvity and yielded the first experimental access to the temperature dependence of the superfluid density in a Fermi superfluid. The propagation of second sound was also the object of a theoretical investigation in two-dimensional bosonic systems where the occurrence of Bose-Einstein condensation is ruled out by thermal fluctuations. The theoretical predictions near the Kosterlitz-Thouless transition are expected to stimulate novel experimental activity in the field. Another important activity concerning transport phenomena was the study of the Kibble-Zurek mechanism and the generation of quantum defects (solitons and solitonic vortices), also in collaboration with the Trento experimental team of G. Ferrari. Remarkable achievements have also been obtained in the field of quantum fluids of light where fundamental superfluid hydrodynamic phenomena and soliton and vortex nucleation have been studied , mostly in collaboration with the A. Bramati and E. Giacobino experimental group at LKB-Paris 6-CNRS. MOTION OF IMPURITIES EMBEDDED IN A QUANTUM GAS. The research project in this direction has mainly focused on the study of binary mixtures of quantum gases with population imbalance and the corresponding predictions for their static and dynamic behavior. In this context both spin polarized Fermi gases and Bose-Fermi mixtures have been investigated, including the study, in the case of polarized Fermi gases, of the spin susceptibility and the Chandrasekhar-Clogston limit. The theoretical studies in this direction have stimulated new scientific collaborations with the experimental team of Christophe Salomon at the LKB laboratory of ENS and have produced some joint scientific papers. The Trento BEC team has been also able to characterize the behavior of impurities in bilayer configurations of fermionic dipoles, using both diagrammatic as well as quantum Monte Carlo techniques. NOVEL PHASES AND QUANTUM SIMULATORS. Within this activity the Trento BEC team has obtained relevant scientific results in the emergent field of spinor Bose gases , artificial gauge fields in both atomic and photonic systems, dipolar gases and condensed matter analogs of gravitational physics. Among the most relevant predictions it is worth mentioning the dynamic behavior of Rabi coupled Bose gases across the transition between the paramagnetic and the ferromagnetic phase, the dramatic softening of the frequency of the dipolar excitation near the transition between the plane wave and the zero-th momentum in spin-orbit coupled (SOC) gases, the identification of supersolid effects in the stripe phase and the emergence of a rotonic structure in the dispersion of the elementary excitations in the plane-wave phase of SOC gases. The theoretical predictions for the softening of the dipolar frequency and for the occurrence of the rotonic excitation have been confirmed experimentally with good accuracy by the Chinese team of S. Chen. Important predictions have also concerned the geometrical and topological properties of the photonic bands of the recently discovered condensed-matter analog models of gravitational physics. TUNNELING, NUMBER VS PHASE DYNAMICS AND QUANTUM CORRELATIONS. This activity has focused on the dynamic behavior of strongly correlated Fermi gases at zero temperature. Significant predictions were obtained for the motion of solitons in harmonic traps which stimulated novel experiments by M. Zwierlein at Mit and the excitation of the Higgs mode and of Josephson oscillations in Fermi superfluids.
