We develop a description of fermionic superfluids in terms of an effective field theory for the pairing order parameter. Our effective field theory improves on the existing Ginzburg -Landau theory for superfluid Fermi gases in that it is not restricted to temperatures close to the critical temperature. This is achieved by taking into account long-range fluctuations to all orders. The results of the present effective field theory compare well with the results obtained in the framework of the Bogoliubov -de Gennes method. The advantage of an effective field theory over Bogoliubov -de Gennes calculations is that much less computation time is required. In the second part of the paper, we extend the effective field theory to the case of a two-band superfluid. The present theory allows us to reveal the presence of two healing lengths in the two-band superfluids, to analyze the finite-temperature vortex structure in the BEC-BCS crossover, and to obtain the ground state parameters and spectra of collective excitations. For the Leggett mode our treatment provides an interpretation of the observation of this mode in two-band superconductors.

In this paper the properties of dark solitons in superfluid Fermi gases with spin-imbalance are studied by means of a recently developed effective field theory [S. N. Klimin et al., Eur. Phys. J. B 88, 122 (2015)] suitable to describe the BEC-BCS crossover in ultracold gases in an extended range of temperatures as compared to the usual Ginzburg-Landau treatments. The spatial profiles for the total density and for the density of the excess-spin component, and the changes of their properties across the BEC-BCS crossover are examined in different conditions of temperature and imbalance. The presence of population imbalance is shown to strongly affect the structure of the soliton excitation by filling its core with unpaired atoms. This in turn influences the dynamical properties of the soliton since the additional particles in the core have to be dragged along thus altering the effective mass.

In this paper the properties of dark solitons in superfluid Fermi gases with spin-imbalance are studied by means of a recently developed effective field theory [S. N. Klimin et al., Eur. Phys. J. B 88, 122 (2015)] suitable to describe the BEC-BCS crossover in ultracold gases in an extended range of temperatures as compared to the usual Ginzburg-Landau treatments. The spatial profiles for the total density and for the density of the excess-spin component, and the changes of their properties across the BEC-BCS crossover are examined in different conditions of temperature and imbalance. The presence of population imbalance is shown to strongly affect the structure of the soliton excitation by filling its core with unpaired atoms. This in turn influences the dynamical properties of the soliton since the additional particles in the core have to be dragged along thus altering the effective mass.

Motivated by the remarkable experimental control of synthetic gauge fields in ultracold atomic systems, we investigate the effect of an artificial Rashba spin-orbit coupling on the spin polarization of a two-dimensional repulsive Fermi gas. By using a variational many-body wave function, based on a suitable spinorial structure, we find that the polarization properties of the system are indeed controlled by the interplay between spin-orbit coupling and repulsive interaction. In particular, two main effects are found: (1) The Rashba coupling determines a gradual increase of the degree of polarization beyond the critical repulsive interaction strength, at variance with conventional two-dimensional Stoner instability. (2) The critical interaction strength, above which finite polarization is developed, shows a dependence on the Rashba coupling, i.e., it is enhanced in case the Rashba coupling exceeds a critical value. A simple analytic expression for the critical interaction strength is further derived in the context of our variational formulation, which allows for a straightforward and insightful analysis of the present problem

In this work dark soliton collisions in a one-dimensional superfluid Fermi gas are studied across the BEC-BCS crossover by means of a recently developed finite-temperature effective field theory (2015 Eur. Phys. J. B 88 122). The evolution of two counter-propagating solitons is simulated numerically based on the theory's nonlinear equation of motion for the pair field. The resulting collisions are observed to introduce a spatial shift into the trajectories of the solitons. The magnitude of this shift is calculated and studied in different conditions of temperature and spin-imbalance. When moving away from the BEC-regime, the collisions are found to become inelastic, emitting the lost energy in the form of small-amplitude density oscillations. This inelasticity is quantified and its behavior analyzed and compared to the results of other works. The dispersion relation of the density oscillations is calculated and is demonstrated to show a good agreement with the spectrum of collective excitations of the superfluid.