We present new results for interacting quantum Fermi gases, confined in an optical lattice. Finite temperature atomic correlations are calculated using a novel Gaussian representation. Luttinger liquid theory and the local density approximation let us calculate collective mode frequencies at the metal-insulator transition.
Experiments with ultracold atoms present an outstanding opportunity for implementing novel tests of theories of strongly correlated fermions. We present three new theoretical methods to treat these systems. Luttinger liquid theory and the exact one-dimensional solutions let us calculate collective mode frequencies at the metal-insulator transition in a lattice. A new Gaussian phase-space method for fermion systems can be used to simulate finite temperature atomic correlations. Finally, we introduce an approximate diagrammatic technique which correctly includes molecule-molecule interactions, and gives an accurate, quantitative theory of the BEC-BCS crossover regime.
Using the exact Bethe ansatz solution of the Hubbard model and Luttinger liquid theory, we investigate the density profiles and collective modes of one-dimensional ultracold fermions confined in an optical lattice with a harmonic trapping potential. We determine a generic phase diagram in terms of a characteristic filling factor and a dimensionless coupling constant. The collective oscillations of the atomic mass density, a technique that is commonly used in experiments, provide a signature of the quantum phase transition from the metallic phase to the Mott-insulator phase. A detailed experimental implementation is proposed.
We present an extensive numerical study of the ground-state properties of confined repulsively interacting fermions in one-dimensional optical lattices. Detailed predictions for the atom-density profiles are obtained from parallel Kohn-Sham density-functional calculations and quantum Monte Carlo simulations. The density-functional calculations employ a Bethe ansatz based local-density approximation for the correlation energy that accounts for Luttinger-liquid and Mott-insulator physics. Semianalytical and fully numerical formulations of this approximation are compared with each other and with a cruder Thomas-Fermi-type local-density approximation for the total energy. Precise quantum Monte Carlo simulations are used to assess the reliability of the various local-density approximations, and in conjunction with these provide a detailed microscopic picture of the consequences of the interplay between particle-particle interactions and confinement in one-dimensional systems of strongly correlated fermions.
We study cold atomic gases with a contact interaction and confined into one-dimension. Crossing the confinement induced resonance the correlation between the bosons increases, and introduces an effective range for the interaction potential. Using the mapping onto the sine-Gordon model and a Hubbard model in the strongly interacting regime allows us to derive the phase diagram in the presence of an optical lattice. We find the appearance of a phase transition from a Luttinger liquid with algebraic correlations into a crystalline phase with a particle on every second lattice site.