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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 [L. Tarruell et al., Nature 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.
Tight-binding models for ultracold atoms in optical lattices can be properly defined by using the concept of maximally localized Wannier functions for composite bands. The basic principles of this approach are reviewed here, along with different appl
We present a framework to elucidate the existence of accidental contacts of energy bands, particularly those called Dirac points which are the point contacts with linear energy dispersions in their vicinity. A generalized von-Neumann-Wigner theorem w
Dirac-Weyl fermions are massless relativistic particles with a well-defined helicity which arise in the context of high-energy physics. Here we propose a quantum simulation of these paradigmatic fermions using multicomponent ultracold atoms in a two-
We experimentally realize Rydberg excitations in Bose-Einstein condensates of rubidium atoms loaded into quasi one-dimensional traps and in optical lattices. Our results for condensates expanded to different sizes in the one-dimensional trap agree we
As the temperature of a many-body system approaches absolute zero, thermal fluctuations of observables cease and quantum fluctuations dominate. Competition between different energies, such as kinetic energy, interactions or thermodynamic potentials,