We study the magnetic ordering transition for a system of harmonically trapped ultracold fermions with repulsive interactions in a cubic optical lattice, within a real-space extension of dynamical mean-field theory. Using a quantum Monte Carlo impurity solver, we establish that antiferromagnetic correlations are signaled, at strong coupling, by an enhanced double occupancy. This signature is directly accessible experimentally and should be observable well above the critical temperature for long-range order. Dimensional aspects appear less relevant than naively expected.
We study magnetic phases of two-component mixtures of ultracold fermions with repulsive interactions in optical lattices in the presence of both hopping and population imbalance by means of dynamical mean-field theory (DMFT). It is shown that these mixtures can have easy-axis antiferromagnetic, ferrimagnetic, charge-density wave, and canted-antiferromagnetic order or be unordered depending on parameters of the system. We study the resulting phase diagram in detail and investigate the stability of the different phases with respect to thermal fluctuations. We also perform a quantitative analysis for a gas confined in a harmonic trap, both within the local density approximation and using a full real-space generalization of DMFT.
We describe the emergence of superfluid phases of ultracold dipolar fermions in optical lattices for two-dimensional systems. Considering the many-body screening of dipolar interactions at intermediate and larger filling factors, we show that several superfluid phases with distinct pairing symmetries naturally arise in the singlet channel: local s-wave
(sl), extended s-wave
(se), d-wave
(d) or time-reversal-symmetry breaking
(sl+se±id)-wave. We obtain the temperature versus filling factor phase diagram and show that d-wave pairing is favored near half-filling, that
(sl+se)-wave is favored near zero or full filling, and that time-reversal-breaking
(sl+se±id)-wave is favored in between. The inclusion of a harmonic trap reveals that a sequence of phases can coexist in the cloud depending on the filling factor at the center of the trap. Most notably in the spatial region where the
(sl+se±id)-wave superfluid occurs, spontaneous currents are generated, and may be detected using velocity sensitive Bragg spectroscopy.