Abstract:
The phase diagram of one-dimensional earth-alkaline fermionic atoms and ytterbium 171 atoms is investigated by means of a low-energy approach and density-matrix renormalization group calculations. For incommensurate filling, four gapless phases with a spin gap are found and consist of two superconducting instabilities and two coexisting bond and charge density-waves instabilities. In the half-filled case, seven Mott-insulating phases arise with the emergence of four non-degenerate phases with exotic hidden orderings.

Abstract:
We consider a few-particle system of trapped neutral fermionic atoms at ultra-low temperatures, with the attractive interaction tuned to Feshbach resonance. We calculate the energies and the spatial densities of the few-body systems using a generalisation of the extended Thomas-Fermi (ETF) method, and assuming the particles obey the Haldane-Wu fractional exclusion statistics (FES) at unitarity. This method is different from the scaled ETF version given by Chang and Bertsch (Phys. Rev. A76,021603(R) (2007)). Our semiclassical FES results are consistent with the Monte-Carlo calculations of the above authors, but can hardly be distinguished from their over all scaling of the ETF result at unitarity.

Abstract:
The major finding of this paper is that a one-dimensional spin-polarized gas comprised of an even number of fermionic atoms interacting via attractive p-wave interactions and confined to a mesoscopic ring has a degenerate pair of ground states that are oppositely rotating. In any realization the gas will thus spontaneously rotate one way or the other in spite of the fact that there is no external rotation or bias fields. Our goal is to show that this counter-intuitive finding is a natural consequence of the combined effects of quantum statistics, ring topology, and exchange interactions.

Abstract:
We consider a generic two-dimensional system of fermionic particles with attractive interactions and no disorder. If time-reversal symmetry is absent, it is possible to obtain incompressible insulating states in addition to the superfluid at zero temperature. The superfluid-insulator phase transition is found to be second order in type-II systems using a perturbative analysis of Cooper pairing instability in quantum Hall states of unpaired fermions. We obtain the pairing phase diagram as a function of chemical potential (density) and temperature. However, a more careful analysis presented here reveals that the pairing quantum phase transition is always preempted by another transition into a strongly correlated normal state which retains Cooper pairing and cannot be smoothly connected to the quantum Hall state of unpaired fermions. Such a normal phase can be qualitatively viewed as a liquid of vortices, although it may acquire conventional broken symmetries. Even if it did not survive at finite temperatures its influence would be felt through strong quantum fluctuations below a crossover temperature scale. These conclusions directly apply to fermionic ultra-cold atom systems near unitarity, but are likely relevant for the properties of other strongly correlated superfluids as well, including high temperature superconductors.

Abstract:
We study the effect of the rotation on a harmonically trapped Fermi gas at zero temperature under the assumption that vortices are not formed. We show that at unitarity the rotation produces a phase separation between a non rotating superfluid (S) core and a rigidly rotating normal (N) gas. The interface between the two phases is characterized by a density discontinuity $n_{\rm N}/n_{\rm S}= 0.85$, independent of the angular velocity. The depletion of the superfluid and the angular momentum of the rotating configuration are calculated as a function of the angular velocity. The conditions of stability are also discussed and the critical angular velocity for the onset of a spontaneous quadrupole deformation of the interface is evaluated.

Abstract:
Fermionic atoms in an optical superlattice can realize a very peculiar Anderson lattice model in which impurities interact with each other through a discretized set of delocalized levels. We investigate the interplay between Kondo effect and magnetism under these finite-size features. We find that Kondo effect can dominate over magnetism depending on the parity of the number of particles per discretized set. We show how Kondo-induced resonances of measurable size can be observed through the atomic interference pattern.

Abstract:
Variational and diffusion quantum Monte Carlo (VMC and DMC) calculations of the properties of the zero-temperature fermionic gas at unitarity are reported. The ratio of the energy of the interacting to the non-interacting gas for a system of 128 particles is calculated to be 0.4517(3) in VMC and 0.4339(1) in the more accurate DMC method. The spherically-averaged pair-correlation functions, momentum densities, and one-body density matrices are very similar in VMC and DMC, but the two-body density matrices and condensate fractions show some differences. Our best estimate of the condensate fraction of 0.51 is a little smaller than values from other quantum Monte Carlo calculations.

Abstract:
We study a class of SU(N) Heisenberg models, describing Mott insulators of fermionic ultra-cold alkaline earth atoms on the three-dimensional simple cubic lattice. Based on an earlier semiclassical analysis, magnetic order is unlikely, and we focus instead on a solvable large-N limit designed to address the competition among non-magnetic ground states. We find a rich phase diagram as a function of the filling parameter k, composed of a variety of ground states spontaneously breaking lattice symmetries, and in some cases also time reversal symmetry. One particularly striking example is a state spontaneously breaking lattice rotation symmetry, where the cubic lattice breaks up into bilayers, each of which forms a two-dimensional chiral spin liquid state.

Abstract:
We predict novel phenomena in the behavior of an ultra- cold, trapped gas of fermionic atoms. We find that quantum statistics radically changes the collisional properties, spatial profile, and off-resonant light scattering properties of the atomic fermion system, and we suggest how these effects can be observed.

Abstract:
We propose an efficient mechanism for the evaporative cooling of trapped fermions directly into quantum degeneracy. Our idea is based on an electric field induced elastic interaction between trapped atoms in spin symmetric states. We discuss some novel general features of fermionic evaporative cooling and present numerical studies demonstrating the feasibility for the cooling of alkali metal fermionic species $^6$Li, $^{40}$K, and $^{82,84,86}$Rb. We also discuss the sympathetic cooling of fermionic hyperfine spin mixtures, including the effects of anisotropic interactions.