Artificial Staggered Magnetic Field for Ultracold Atoms in Optical Lattices

A time-dependent optical lattice with staggered particle current in the tight-binding regime was considered that can be described by a time-independent effective lattice model with an artificial staggered magnetic field. The low energy description of a single-component fermion in this lattice at half-filling is provided by two copies of ideal two-dimensional massless Dirac fermions. The Dirac cones are generally anisotropic and can be tuned by the external staggered flux \p. For bosons, the staggered flux modifies the single-particle spectrum such that in the weak coupling limit, depending on the flux \p, distinct superfluid phases are realized. Their properties are discussed, the nature of the phase transitions between them is establised, and Bogoliubov theory is used to determine their excitation spectra. Then the generalized superfluid-Mott-insulator transition is studied in the presence of the staggered flux and the complete phase diagram is established. Finally, the momentum distribution of the distinct superfluid phases is obtained, which provides a clear experimental signature of each phase in ballistic expansion experiments.Comment: 14 pages, 5 figure

Internal Josephson Oscillations for Distinct Momenta Bose-Einstein Condensates

The internal Josephson oscillations between an atomic Bose-Einstein condensate (BEC) and a molecular one are studied for atoms in a square optical lattice subjected to a staggered gauge field. The system is described by a Bose-Hubbard model with complex and anisotropic hopping parameters that are different for each species, i.e., atoms and molecules. When the flux per plaquette for each species is small, the system oscillates between two conventional zero-momentum condensates. However, there is a regime of parameters in which Josephson oscillations between a vortex-carrying atomic condensate (finite momentum BEC) and a conventional zero-momentum molecular condensate may be realized. The experimental observation of the oscillations between these qualitatively distinct BEC's is possible with state-of-the-art Ramsey interference techniques.Comment: 8 pages, 6 figure

Competing Superconducting States for Ultracold Atoms in Optical Lattices with Artificial Staggered Magnetic Field

We study superconductivity in an ultracold Bose-Fermi mixture loaded into a square optical lattice subjected to a staggered flux. While the bosons form a superfluid at very low temperature and weak interaction, the interacting fermions experience an additional long-ranged attractive interaction mediated by phonons in the bosonic superfluid. This leads us to consider a generalized Hubbard model with on-site and nearest-neighbor attractive interactions, which give rise to two competing superconducting channels. We use the Bardeen-Cooper-Schrieffer theory to determine the regimes where distinct superconducting ground states are stabilized, and find that the non-local pairing channel favors a superconducting ground state which breaks both the gauge and the lattice symmetries, thus realizing unconventional superconductivity. Furthermore, the particular structure of the single-particle spectrum leads to unexpected consequences, for example, a dome-shaped superconducting region in the temperature versus filing fraction phase diagram, with a normal phase that comprises much richer physics than a Fermi-liquid. Notably, the relevant temperature regime and coupling strength is readily accessible in state of the art experiments with ultracold trapped atoms

Spin- and band-ferromagnetism in trilayer graphene

We study the ground state properties of an ABA-stacked trilayer graphene. The low energy band structure can be described by a combination of both a linear and a quadratic particle-hole symmetric dispersions, reminiscent of monolayer- and bilayer-graphene, respectively. The multi-band structure offers more channels for instability towards ferromagnetism when the Coulomb interaction is taken into account. Indeed, if one associates a pseudo-spin 1/2 degree of freedom to the bands (parabolic/linear), it is possible to realize also a band-ferromagnetic state, where there is a shift in the energy bands, since they fill up differently. By using a variational procedure, we compute the exchange energies for all possible variational ground states and identify the parameter space for the occurrence of spin- and band-ferromagnetic instabilities as a function of doping and interaction strength.Comment: 9 pages/ 8 figure