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We investigate the dynamics of a wave packet in a parity-breaking one-dimensional periodic potential slowly varied in time and perturbed by a linear potential. Parity is broken by considering an asymmetric double well per unit cell. By comparing the prediction of the semiclassical dynamics with the full Schrödinger solution, we show that Bloch oscillations are strongly affected by anomalous velocity corrections related to Berry's phase. We characterize how these effects depend on the degree of parity breaking of the potential and on the modulation parameters. We also discuss how to measure the effects of the anomalous velocity in current experiments with noninteracting Bose-Einstein condensates in bichromatic optical lattices, under the effect of gravity. [ABSTRACT FROM AUTHOR]

The physics of one-dimensional optical superlattices with resonant s-p orbitals is reexamined in the language of appropriate Wannier functions. It is shown that details of the tight-binding model realized in different optical potentials crucially depend on the proper determination of Wannier functions. We discuss the properties of a superlattice model which quasiresonantly couples s and p orbitals and show its relation with different tight-binding models used in other works. [ABSTRACT FROM AUTHOR]

We review the derivation of the effective Dirac equation for ultracold atoms in one-dimensional bichromatic optical lattices, following the proposal by Witthaut et al. [Phys. Rev. A 84, 033601 (2011)]. We discuss how such a derivation--based on a suitable rotation of the Bloch basis and on a coarse-graining approximation--is affected by the choice of the Wannier functions entering the coarsening procedure. We show that in general the Wannier functions obtained by rotating the maximally localized Wannier functions for the original Bloch bands can be sufficiently localized for justifying the coarse-graining approximation. We also comment on the relation between the rotation needed to achieve the Dirac form and the standard Foldy-Wouthuysen transformation. Our results provide a solid ground for the interpretation of the experimental results by Salger et al. [Phys. Rev. Lett. 107, 240401 (2011)] in terms of an effective Dirac dynamics. [ABSTRACT FROM AUTHOR]

We present two independent approaches for calculating the tight-binding parameters of the Haldane model with ultracold atoms. The tunneling coefficients up to next-nearest neighbors are computed ab initio by using the maximally localized Wannier functions and compared to analytical expressions written in terms of gauge-invariant measurable properties of the spectrum. The two approaches present a remarkable agreement and evidence the breakdown of the Peierls substitution: (i) the phase acquired by the next-nearest tunneling amplitude t1 presents quantitative and qualitative differences with respect to that obtained by the integral of the vector field A, as considered in the Peierls substitution, even in the regime of low amplitudes of A; and (ii) for larger values, also |ti| and the nearest-neighbor tunneling t0 have a marked dependence on A. The origin of this behavior and its implications are discussed. [ABSTRACT FROM AUTHOR]

We present an accurate ab initio tight-binding model, capable of describing the dynamics of Dirac points in tunable honeycomb optical lattices following a recent experimental realization [ Tarruell et al. Nature (London) 483 302 (2012)]. Our scheme is based on first-principle maximally localized Wannier functions for composite bands. The tunneling coefficients are calculated for different lattice configurations, and the spectrum properties are well reproduced with high accuracy. In particular, we show which tight-binding description is needed in order to accurately reproduce the position of Dirac points and the dispersion law close to their merging, for different laser intensities. [ABSTRACT FROM AUTHOR]

We discuss how to construct tight-binding models for ultracold atoms in honeycomb potentials, by means of the maximally localized Wannier functions (MLWFs) for composite bands introduced by Marzari and Vanderbilt [Phys. Rev. B 56, 12847 (1997)]. In particular, we work out the model with up to third-nearest neighbors, and provide explicit calculations of the MLWFs and of the tunneling coefficients for the graphenelike potential with two degenerate minima per unit cell. Finally, we discuss the degree of accuracy in reproducing the exact Bloch spectrum of different tight-binding approximations, in a range of typical experimental parameters. [ABSTRACT FROM AUTHOR]