Two-body problem in periodic potentials

We investigate the problem of two atoms interacting via a short range s-wave potential in the presence of a deep optical lattice of arbitrary dimension $D$. Using a tight binding approach, we derive analytical results for the properties of the bound state and the scattering amplitude. We show that the tunneling through the barriers induces a dimensional crossover from a confined regime at high energy to an anisotropic three dimensional regime at low energy. The critical value of the scattering length needed to form a two-body bound state shows a logaritmic dependence on the tunneling rate for D=1 and a power law for $D>1$. For the special case D=1, we also compare our analytical predictions with exact numerics, finding remarkably good agreement

BCS-BEC crossover in a random external potential

We investigate the ground state properties of a disordered superfluid Fermi gas across the BCS-BEC (Bose Einstein condensate) crossover. We show that, for weak disorder, both the depletion of the condensate fraction of pairs and the normal fluid density exhibit a nonmonotonic behavior as a function of the interaction parameter $1/k_Fa$, reaching their minimum value near unitarity. We find that, moving away from the weak coupling BCS regime, Anderson's theorem ceases to apply and the superfluid order parameter is more and more affected by the random potential.Comment: Revised version, one reference added, Phys. Rev. Lett. in pres

Lattice modulation spectroscopy of strongly interacting bosons in disordered and quasi-periodic optical lattices

We compute the absorption spectrum of strongly repulsive one-dimensional bosons in a disordered or quasi-periodic optical lattice. At commensurate filling, the particle-hole resonances of the Mott insulator are broadened as the disorder strength is increased. In the non-commensurate case, mapping the problem to the Anderson model allows us to study the Bose-glass phase. Surprisingly we find that a perturbative treatment in both cases, weak and strong disorder, gives a good description at all frequencies. In particular we find that the infrared absorption rate in the thermodynamic limit is quadratic in frequency. This result is unexpected, since for other quantities like the conductivity in one dimensional systems, perturbation theory is only applicable at high frequencies. We discuss applications to recent experiments on optical lattice systems, and in particular the effect of the harmonic trap.Comment: 11 pages, 8 figure

Transport Properties in the "Strange Metal Phase" of High Tc Cuprates: Spin-Charge Gauge Theory Versus Experiments

The SU(2)xU(1) Chern-Simons spin-charge gauge approach developed earlier to describe the transport properties of the cuprate superconductors in the ``pseudogap'' regime, in particular, the metal-insulator crossover of the in-plane resistivity, is generalized to the ``strange metal'' phase at higher temperature/doping. The short-range antiferromagnetic order and the gauge field fluctuations, which were the key ingredients in the theory for the pseudogap phase, also play an important role in the present case. The main difference between these two phases is caused by the existence of an underlying statistical $\pi$-flux lattice for charge carriers in the former case, whereas the background flux is absent in the latter case. The Fermi surface then changes from small ``arcs'' in the pseudogap to a rather large closed line in the strange metal phase. As a consequence the celebrated linear in T dependence of the in-plane and out-of-plane resistivity is shown explicitly to recover. The doping concentration and temperature dependence of theoretically calculated in-plane and out-of-plane resistivity, spin-relaxation rate and AC conductivity are compared with experimental data, showing good agreement.Comment: 14 pages, 5 .eps figures, submitted to Phys. Rev. B, revised version submitted on 24 Oc

Equilibrium and dynamics of a trapped superfluid Fermi gas with unequal masses

Interacting Fermi gases with equal populations but unequal masses are investigated at zero temperature using local density approximation and the hydrodynamic theory of superfluids in the presence of harmonic trapping. We derive the conditions of energetic stability of the superfluid configuration with respect to phase separation and the frequencies of the collective oscillations in terms of the mass ratio and the trapping frequencies of the two components. We discuss the behavior of the gas after the trapping potential of a single component is switched off and show that, near a Feshbach resonance, the released component can still remain trapped due to many-body interaction effects. Explicit predictions are presented for a mixture of $^6$Li and $^{40}$K with resonant interaction.Comment: 4 pages, 2 figure

Attractive Fermi gases with unequal spin populations in highly elongated traps

We investigate two-component attractive Fermi gases with imbalanced spin populations in trapped one dimensional configurations. The ground state properties are determined within local density approximation, starting from the exact Bethe-ansatz equations for the homogeneous case. We predict that the atoms are distributed according to a two-shell structure: a partially polarized phase in the center of the trap and either a fully paired or a fully polarized phase in the wings. The partially polarized core is expected to be a superfluid of the FFLO type. The size of the cloud as well as the critical spin polarization needed to suppress the fully paired shell, are calculated as a function of the coupling strength.Comment: Final accepted versio

Achieving one-dimensionality with attractive fermions

In this article we discuss the accuracy of effective one-dimensional theories used to describe the behavior of ultracold atomic ensembles confined in quantum wires by a harmonic trap. We derive within a fully many-body approach the effective Hamiltonian describing this class of systems and we calculate the beyond-mean field corrections to the energy of the ground state arising from virtual transitions towards excited state of the confining potential. We find that, due to the Pauli principle, effective finite-range corrections are one of magnitude larger than effective three-body interactions.By comparing to exact solutions of the purely 1D problem, we conclude that a 1D effective theory provides a good description of the ground state of the system for a rather large range of interaction parameters

Umklapp collisions and center of mass oscillation of a trapped Fermi gas

Starting from the the Boltzmann equation, we study the center of mass oscillation of a harmonically trapped normal Fermi gas in the presence of a one-dimensional periodic potential. We show that for values of the the Fermi energy above the first Bloch band the center of mass motion is strongly damped in the collisional regime due to umklapp processes. This should be contrasted with the behaviour of a superfluid where one instead expects the occurrence of persistent Josephson-like oscillations.Comment: 11 pages, 3 figures, corrected typo

Quantum Monte Carlo simulations of two-dimensional repulsive Fermi gases with population imbalance

The ground-state properties of two-component repulsive Fermi gases in two dimensions are investigated by means of fixed-node diffusion Monte Carlo simulations. The energy per particle is determined as a function of the intercomponent interaction strength and of the population imbalance. The regime of universality in terms of the s-wave scattering length is identified by comparing results for hard-disk and for soft-disk potentials. In the large imbalance regime, the equation of state turns out to be well described by a Landau-Pomeranchuk functional for two-dimensional polarons. To fully characterize this expansion, we determine the polarons' effective mass and their coupling parameter, complementing previous studies on their chemical potential. Furthermore, we extract the magnetic susceptibility from low-imbalance data, finding only small deviations from the mean-field prediction. While the mean-field theory predicts a direct transition from a paramagnetic to a fully ferromagnetic phase, our diffusion Monte Carlo results suggest that the partially ferromagnetic phase is stable in a narrow interval of the interaction parameter. This finding calls for further analyses on the effects due to the fixed-node constraint.Comment: 10 pages, 5 figure