The polarization produced by the relative displacement of the potentials trapping two spin species of a dilute Fermi gas with N=N is calculated at unitarity by assuming phase separation between the superfluid and a polarized phase at zero temperature. Because of the energy cost associated with pair breaking, the dipole polarizability is strongly quenched and exhibits important deviations from the ideal gas behavior even for nonlinear displacements of the order of the size of the atomic cloud. The behavior in the presence of different trapping frequencies (monopole polarization) for the two spin species is also discussed. Our results suggest new experimental perspectives to explore the quantum phases of interacting Fermi gases.
The polarization produced by the relative displacement of the potentials trapping two spin species of a dilute Fermi gas with N=N is calculated at unitarity by assuming phase separation between the superfluid and a polarized phase at zero temperature. Because of the energy cost associated with pair breaking, the dipole polarizability is strongly quenched and exhibits important deviations from the ideal gas behavior even for nonlinear displacements of the order of the size of the atomic cloud. The behavior in the presence of different trapping frequencies (monopole polarization) for the two spin species is also discussed. Our results suggest new experimental perspectives to explore the quantum phases of interacting Fermi gases.
We study the Fermi gas at unitarity and at T=0 by assuming that, at high polarizations, it is a normal Fermi liquid composed of weakly interacting quasiparticles associated with the minority spin atoms. With a quantum Monte Carlo approach we calculate their effective mass and binding energy, as well as the full equation of state of the normal phase as a function of the concentration x=n downward arrow/n upward arrow of minority atoms. We predict a first order phase transition from normal to superfluid at x(c)=0.44 corresponding, in the presence of harmonic trapping, to a critical polarization P(c)=(N upward arrow - N downward arrow/(N upward arrow + N downward arrow)=77%. We calculate the radii and the density profiles in the trap and predict that the frequency of the spin dipole mode will be increased by a factor of 1.23 due to interactions.
In this thesis we first review the theory of the normal state of the unitary Fermi gas at T = 0 and the main properties of the normal-to-superfluid transition. Then we study the trapped gas under adiabatic rotation, i.e., avoiding the formation of vortices. We show that for polarized systems the rotation enhances the Chandrasekhar-Clogston limit due to pair breaking at the border between the superfluid and the normal phase, while it leaves the global critical polarization Pc of the trapped system unaffected. In the case of an unpolarized unitary superfluid the rotation causes a phase separation between a superfluid core and an unpolarized normal shell, in which the densities of the spin-up and spin-down atom numbers is equal. For both the polarized and the unpolarized systems we calculate experimental observables such as the density profiles and the angular momenta. From the study of Bose-Einstein condensates it is well known that an adiabatic rotation induces a quadrupole deformation of the trapped atomic cloud when the rotation exceeds a certain angular velocity. In Fermi gases the situation is different due to the phase separation discussed above, and the quadrupole instabilities are found to set on at smaller angular velocity than in the BEC case. This phenomenon together with a more general discussion concerning not only the energetic but also the dynamic instabilities of the phase separated system is presented. We use the present knowledge of the equation of state of Fermi mixtures with unequal masses to give quantitative predictions for the phase separation between the normal and superfluid components. The analysis is based on the study of the zero temperature μ-h phase diagram of the uniform two component gas. The phase diagram at unitarity is determined thanks to the knowledge of the equation of state available from diagrammatic techniques applied to highly polarized configurations and from Monte Carlo simulations. The phase diagram is then used, in the local density approximation, to calculate the density profiles of the two Fermi components in the presence of harmonic trapping. Eventually we investigate the polarization produced by the relative displacement of the potentials trapping two spin species of a unitary Fermi gas with population imbalance. We investigate the dipole polarizability of a polarized system both in the two-fluid and the three-fluid model at zero temperature and point out the major differences between the two treatments.
We study the zero temperature properties of a trapped polarized Fermi gas at unitarity by assuming phase separation between an unpolarized superfluid and a polarized normal phase. The effects of the interaction are accounted for using the formalism of quasiparticles to build up the equation of state of the normal phase with the Monte Carlo results for the relevant parameters. Our predictions for the Chandrasekhar-Clogston limit of critical polarization and for the density profiles, including the density jump at the interface, are confirmed with excellent accuracy by the recent experimental results at MIT. The role of interaction on the radial width of the minority component, on the gap of spectral functions, and on the spin oscillations in the normal phase is also discussed. Our analysis points out the Fermi liquid nature of these strongly interacting spin-polarized configurations.
Superconductivity and superfluidity of fermions require, within the BCS theory, matching of the Fermi energies of the two interacting Fermion species. Difference in the number densities of the two species leads either to a normal state, to phase separation, or---potentially---to exotic forms of superfluidity such as Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state, Sarma state, or breached pair state. We consider ultracold Fermi gases with polarization, i.e., spin-density imbalance. We show that, due to the gases being trapped and isolated from the environment in terms of particle exchange, exotic forms of superfluidity appear as a shell around the Bardeen-Cooper-Schrieffer (BCS) superfluid core of the gas and, for large density imbalance, in the core as well. We obtain these results by describing the effect of the trapping potential by using the Bogoliubov-de Gennes equations. For comparison to experiments, we calculate also the condensate fraction, and show that, in the center of the trap, a polarized superfluid leads to a small dip in the central density difference. We compare the results to those given by local density approximation and find qualitatively different behavior.
We theoretically investigate the spin-dipole oscillation of a strongly interacting Fermi gas confined by a harmonic trapping potential. By using a diagrammatic strong-coupling theory combined with a local density approximation and a sum rule approach, we study the temperature dependence of the spin-dipole frequency near unitarity. The connection of the spin-dipole frequency with the spin susceptibility and the pairing correlations is exploited. While the spin-dipole frequency exactly coincides with the trap frequency in a noninteracting Fermi gas, it is shown to be strongly enhanced in the superfluid state, because of the suppression of the spin degree of freedom due to the spin-singlet Cooper-pair formation. In strongly interacting Fermi gases, such enhancement occurs even above the superfluid phase transition temperature, due to the strong pairing correlations.
The physics of quantum degenerate atomic Fermi gases in uniform as well as in harmonically trapped configurations is reviewed from a theoretical perspective. Emphasis is given to the effect of interactions that play a crucial role, bringing the gas into a superfluid phase at low temperature. In these dilute systems, interactions are characterized by a single parameter, the s-wave scattering length, whose value can be tuned using an external magnetic field near a broad Feshbach resonance. The BCS limit of ordinary Fermi superfluidity, the Bose-Einstein condensation (BEC) of dimers, and the unitary limit of large scattering length are important regimes exhibited by interacting Fermi gases. In particular, the BEC and the unitary regimes are characterized by a high value of the superfluid critical temperature, on the order of the Fermi temperature. Different physical properties are discussed, including the density profiles and the energy of the ground-state configurations, the momentum distribution, the fraction of condensed pairs, collective oscillations and pair-breaking effects, the expansion of the gas, the main thermodynamic properties, the behavior in the presence of optical lattices, and the signatures of superfluidity, such as the existence of quantized vortices, the quenching of the moment of inertia, and the consequences of spin polarization. Various theoretical approaches are considered, ranging from the mean-field description of the BCS-BEC crossover to nonperturbative methods based on quantum Monte Carlo techniques. A major goal of the review is to compare theoretical predictions with available experimental results.