Making a spin-difference in quantum gases

This thesis studies the theory of quantum gases. We focus on fermionic superfluidity in systems in which the control over the spin degree of freedom has a central role. We explain the microscopic origin of the spin-asymmetric Josephon effect, and propose methods for realizing this effect experimentally in quantum gases. We investigate the phenomenon of fermionic superfluidity in the presence of spin-polarization, with our main focus on the Fulde-Ferrel-Larkin-Ovchinnikov (FFLO) phase. We show that the FFLO pairing mechanism leads to an anisotropic speed of sound which can be used to identify the state in experiments. Using real-space dynamical mean field theory (DMFT), we compute the phase diagram of a trapped, spin-polarized Fermi gas in a dimensional crossover from a 1D to a 3D optical lattice. We find that the FFLO state is realized in a broad region of parameters throughout the crossover while the shell structure of the Fermi gas preceding the transition to the full FFLO state shows a strong dependence on the dimensionality. Finally, we utilize the cluster DMFT method to show that the FFLO state is stable against non-local quantum fluctuations even though these fluctuations do affect the critical temperature of the state.