1,220 research outputs found
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 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
spin-orbit couplings always lead to time-reversal symmetric Hubbard
models, and thereby to topologically trivial band structures, suitable
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
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
Dynamics of localized waves in 1D random potentials: statistical theory of the coherent forward scattering peak
As recently discovered [PRL 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 -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
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
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 -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
Coherent backscattering in nonlinear atomic media: quantum Langevin approach
In this theoretical paper, we investigate coherence properties of the
near-resonant light scattered by two atoms exposed to a strong monochromatic
field. To properly incorporate saturation effects, we use a quantum Langevin
approach. In contrast to the standard optical Bloch equations, this method
naturally provides the inelastic spectrum of the radiated light induced by the
quantum electromagnetic vacuum fluctuations. However, to get the right spectral
properties of the scattered light, it is essential to correctly describe the
statistical properties of these vacuum fluctuations. Because of the presence of
the two atoms, these statistical properties are not Gaussian : (i) the spatial
two-points correlation function displays a speckle-like behavior and (ii) the
three-points correlation function does not vanish. We also explain how to
incorporate in a simple way propagation with a frequency-dependent scattering
mean-free path, meaning that the two atoms are embedded in an average
scattering dispersive medium. Finally we show that saturation-induced
nonlinearities strongly modify the atomic scattering properties and, as a
consequence, provide a source of decoherence in multiple scattering. This is
exemplified by considering the coherent backscattering configuration where
interference effects are blurred by this decoherence mechanism. This leads to a
decrease of the so-called coherent backscattering enhancement factor.Comment: 19 pages, 1 figur
Analytical and numerical study of uncorrelated disorder on a honeycomb lattice
We consider a tight-binding model on the regular honeycomb lattice with
uncorrelated on-site disorder. We use two independent methods (recursive
Green's function and self-consistent Born approximation) to extract the
scattering mean free path, the scattering mean free time, the density of states
and the localization length as a function of the disorder strength. The two
methods give excellent quantitative agreement for these single-particle
properties. Furthermore, a finite-size scaling analysis reveals that all
localization lengths for different lattice sizes and different energies
(including the energy at the Dirac points) collapse onto a single curve, in
agreement with the one-parameter scaling theory of localization. The
predictions of the self-consistent theory of localization however fail to
quantitatively reproduce these numerically-extracted localization lengths.Comment: 19 pages, 25 figure
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