SU(3)SU(3) Topological Insulators in the Honeycomb Lattice

We investigate realizations of topological insulators with spin-1 bosons loaded in a honeycomb optical lattice and subjected to a $SU(3)$ spin-orbit coupling - a situation which can be realized experimentally using cold atomic gases. In this paper, we focus on the topological properties of the single-particle band structure, namely Chern numbers (lattice with periodic boundary conditions) and edge states (lattice with strip geometry). While $SU(2)$ spin-orbit couplings always lead to time-reversal symmetric Hubbard models, and thereby to topologically trivial band structures, suitable $SU(3)$ spin-orbit couplings can break time reversal symmetry and lead to topologically non-trivial bulk band structures and to edge states in the strip geometry. In addition, we show that one can trigger a series of topological transitions (i.e. integer changes of the Chern numbers) that are specific to the geometry of the honeycomb lattice by varying a single parameter in the Hamiltonian.Comment: 12 pages, 8 figure

Topological quantum phase transitions of attractive spinless fermions in a honeycomb lattice

We investigate a spinless Fermi gas trapped in a honeycomb optical lattice with attractive nearest-neighbor interactions. At zero temperature, mean-field theory predicts three quantum phase transitions, two being topological. At low interactions, the system is semi-metallic. Increasing the interaction further, the semi-metal destabilizes into a fully gapped superfluid. At larger interactions, a topological transition occurs and this superfluid phase becomes gapless, with Dirac-like dispersion relations. Finally, increasing again the interaction, a second topological transition occurs and the gapless superfluid is replaced by a different fully gapped superfluid phase. We analyze these different quantum phases as the temperature and the lattice filling are varied.Comment: 6 pages, 5 figure

Triangular and Honeycomb Lattices of Cold Atoms in Optical Cavities

We consider a two-dimensional homogeneous ensemble of cold bosonic atoms loaded inside two optical cavities and pumped by a far-detuned external laser field. We examine the conditions for these atoms to self-organize into triangular and honeycomb lattices as a result of superradiance. By collectively scattering the pump photons, the atoms feed the initially empty cavity modes. As a result, the superposition of the pump and cavity fields creates a space-periodic light-shift external potential and atoms self-organize into the potential wells of this optical lattice. Depending on the phase of the cavity fields with respect to the pump laser, these minima can either form a triangular or a hexagonal lattice. By numerically solving the dynamical equations of the coupled atom-cavity system, we have shown that the two stable atomic structures at long times are the triangular lattice and the honeycomb lattice with equally-populated sites. We have also studied how to drive atoms from one lattice structure to another by dynamically changing the phase of the cavity fields with respect to the pump laser

Momentum-space dynamics of Dirac quasiparticles in correlated random potentials: Interplay between dynamical and Berry phases

We consider Dirac quasi-particles, as realized with cold atoms loaded in a honeycomb lattice or in a $\pi$-flux square lattice, in the presence of a weak correlated disorder such that the disorder fluctuations do not couple the two Dirac points of the lattices. We numerically and theoretically investigate the time evolution of the momentum distribution of such quasi-particles when they are initially prepared in a quasi-monochromatic wave packet with a given mean momentum. The parallel transport of the pseudo-spin degree of freedom along scattering paths in momentum space generates a geometrical phase which alters the interference associated with reciprocal scattering paths. In the massless case, a well-known dip in the momentum distribution develops at backscattering (respective to the Dirac point considered) around the transport mean free time. This dip later vanishes in the honeycomb case because of trigonal warping. In the massive case, the dynamical phase of the scattering paths becomes crucial. Its interplay with the geometrical phase induces an additional transient broken reflection symmetry in the momentum distribution. The direction of this asymmetry is a property of the Dirac point considered, independent of the energy of the wave packet. These Berry phase effects could be observed in current cold atom lattice experiments.Comment: Additional data and explanations compared to version 1. See published article for the latest versio

Half-skyrmion and meron pair in spinor condensates

We propose a simple experimental scheme to generate spin textures in the ground state of interacting ultracold bosonic atoms loaded in a two-dimensional harmonic trap. Our scheme is based on two co-propagating Laguerre-Gauss laser beams illuminating the atoms and coupling two of their internal ground state Zeeman sublevels. Using a Gross-Pitaevskii description, we show that the ground state of the atomic system has different topological properties depending on the interaction strength and the laser beam intensity. A half-skyrmion state develops at low interactions while a meron pair develops at large interactions.Comment: 7 pages, 7 figure

Dynamics of localized waves in 1D random potentials: statistical theory of the coherent forward scattering peak

As recently discovered [PRL ${\bf 109}$ 190601(2012)], Anderson localization in a bulk disordered system triggers the emergence of a coherent forward scattering (CFS) peak in momentum space, which twins the well-known coherent backscattering (CBS) peak observed in weak localization experiments. Going beyond the perturbative regime, we address here the long-time dynamics of the CFS peak in a 1D random system and we relate this novel interference effect to the statistical properties of the eigenfunctions and eigenspectrum of the corresponding random Hamiltonian. Our numerical results show that the dynamics of the CFS peak is governed by the logarithmic level repulsion between localized states, with a time scale that is, with good accuracy, twice the Heisenberg time. This is in perfect agreement with recent findings based on the nonlinear $\sigma$-model. In the stationary regime, the width of the CFS peak in momentum space is inversely proportional to the localization length, reflecting the exponential decay of the eigenfunctions in real space, while its height is exactly twice the background, reflecting the Poisson statistical properties of the eigenfunctions. Our results should be easily extended to higher dimensional systems and other symmetry classes.Comment: See the published article for the updated versio