A self-consistent Hartree-Fock approach for interacting bosons in optical lattices

A theoretical study of interacting bosons in a periodic optical lattice is presented. Instead of the commonly used tight-binding approach (applicable near the Mott insulating regime of the phase diagram), the present work starts from the exact single-particle states of bosons in a cubic optical lattice, satisfying the Mathieu equation, an approach that can be particularly useful at large boson fillings. The effects of short-range interactions are incorporated using a self-consistent Hartree-Fock approximation, and predictions for experimental observables such as the superfluid transition temperature, condensate fraction, and boson momentum distribution are presented.Comment: 12 pages, 15 figure file

Induced p-wave superfluidity in strongly interacting imbalanced Fermi gases

The induced interaction among the majority spin species, due to the presence of the minority species, is computed for the case of a population-imbalanced resonantly-interacting Fermi gas. It is shown that this interaction leads to an instability, at low temperatures, of the recently observed polaron Fermi liquid phase of strongly imbalanced Fermi gases to a p-wave superfluid state. We find that the associated transition temperature, while quite small in the weakly interacting BCS regime, is experimentally accessible in the strongly interacting unitary regime.Comment: Published versio

Observation of Vortex Pinning in Bose-Einstein Condensates

We report the observation of vortex pinning in rotating gaseous Bose-Einstein condensates (BEC). The vortices are pinned to columnar pinning sites created by a co-rotating optical lattice superimposed on the rotating BEC. We study the effects of two different types of optical lattice, triangular and square. With both geometries we see an orientation locking between the vortex and the optical lattices. At sufficient intensity the square optical lattice induces a structural cross-over in the vortex lattice.Comment: 4 pages, 6 figures. Replaced by final version to appear in Phys. Rev. Let

Vortex Lattice Inhomogeneity in Spatially Inhomogeneous Superfluids

A trapped degenerate Bose gas exhibits superfluidity with spatially nonuniform superfluid density. We show that the vortex distribution in such a highly inhomogeneous rotating superfluid is nevertheless nearly uniform. The inhomogeneity in vortex density, which diminishes in the rapid-rotation limit, is driven by the discrete way vortices impart angular momentum to the superfluid. This effect favors highest vortex density in regions where the superfluid density is most uniform (e.g., the center of a harmonically trapped gas). A striking consequence of this is that the boson velocity deviates from a rigid-body form exhibiting a radial-shear flow past the vortex lattice.Comment: 5 RevTeX pgs,2 figures, published versio

Induced superfluidity of imbalanced Fermi gases near unitarity

The induced intraspecies interactions among the majority species, mediated by the minority species, is computed for a population-imbalanced two-component Fermi gas. Although the Feshbach-resonance mediated interspecies interaction is dominant for equal populations, leading to singlet s-wave pairing, we find that in the strongly imbalanced regime the induced intraspecies interaction leads to p-wave pairing and superfluidity of the majority species. Thus, we predict that the observed spin-polaron Fermi liquid state in this regime is unstable to p-wave superfluidity, in accordance with the results of Kohn and Luttinger, below a temperature that, near unitarity, we find to be within current experimental capabilities. Possible experimental signatures of the p-wave state using radio-frequency spectroscopy as well as density-density correlations after free expansion are presented.Comment: 15 pages, 13 figures, submitted to Phys. Rev.

Atom-molecule coherence in a one-dimensional system

We study a model of one-dimensional fermionic atoms that can bind in pairs to form bosonic molecules. We show that at low energy, a coherence develops between the molecule and fermion Luttinger liquids. At the same time, a gap opens in the spin excitation spectrum. The coherence implies that the order parameters for the molecular Bose-Einstein Condensation and the atomic BCS pairing become identical. Moreover, both bosonic and fermionic charge density wave correlations decay exponentially, in contrast with a usual Luttinger liquid. We exhibit a Luther-Emery point where the systems can be described in terms of noninteracting pseudofermions. At this point, we provide closed form expressions for the density-density response functions.Comment: 5 pages, no figures, Revtex 4; (v2) added a reference to cond-mat/0505681 where related results are reported; (v3) Expression of correlation functions given in terms of generalized hypergeometric function

Inhomogeneous superconducting states of mesoscopic thin-walled cylinders in external magnetic fields

We theoretically investigate the appearance of spatially modulated superconducting states in mesoscopic superconducting thin-wall cylinders in a magnetic field at low temperatures. Quantization of the electron motion around the circumference of the cylinder leads to a discontinuous evolution of the spatial modulation of the superconducting order parameter along the transition line Tc(H). We show that this discontinuity leads to the nonmonotonic behavior of the specific heat jump at the onset of superconductivity as a function of temperature and field. We argue that this geometry provides an excellent opportunity to directly and unambiguously detect distinctive signatures of the Fulde-Ferrell-Larkin-Ovchinnikov modulation of the superconducting order. © 2013 American Physical Society

Trapped imbalanced fermionic superfluids in one dimension: A variational approach

We propose and analyze a variational wave function for a population-imbalanced one-dimensional Fermi gas that allows for Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) type pairing correlations among the two fermion species, while also accounting for the harmonic confining potential. In the strongly interacting regime, we find large spatial oscillations of the order parameter, indicative of an FFLO state. The obtained density profiles versus imbalance are consistent with recent experimental results as well as with theoretical calculations based on combining Bethe ansatz with the local density approximation. Our variational wave function displays no signature of the FFLO state in the densities of the two fermion species. Nonetheless, the oscillations of the order parameter appear in density-density correlations, both in situ and after free expansion. Furthermore, above a critical polarization, the value of which depends on the interaction, we find the unpaired Fermi-gas state to be energetically more favorable