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Tight-binding models for ultracold atoms in optical lattices: general formulation and applications

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Abstract

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 applications to lattice potentials with two minima per unit cell, in one and two spatial dimensions. Two independent methods for computing the tight-binding coefficients—one ab initio, based on the maximally localized Wannier functions, the other through analytic expressions in terms of the energy spectrum—are considered. In the one dimensional case, where the tight-binding coefficients can be obtained by designing a specific gauge transformation, we consider both the case of quasi resonance between the two lowest bands, and that between s and p orbitals. In the latter case, the role of the Wannier functions in the derivation of an effective Dirac equation is also reviewed. Then, we consider the case of a two dimensional honeycomb potential, with particular emphasis on the Haldane model, its phase diagram, and the breakdown of the Peierls substitution. Tunable honeycomb lattices, characterized by movable Dirac points, are also considered. Finally, general considerations for dealing with the interaction terms are presented.

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Authors and Affiliations

  1. Departamento de Fisica Teórica e Historia de la Ciencia, Universidad del Pais Vasco UPV/EHU, Bilbao, 48080, Spain

    Michele Modugno

  2. IKERBASQUE, Basque Foundation for Science, Bilbao, 48011, Spain

    Michele Modugno

  3. Peter Grünberg Institute and Institute for Advanced Simulation, Forschungszentrum Jülich & JARA, Jülich, D-52425, Germany

    Julen Ibañez-Azpiroz

  4. Dipartimento di Fisica e Astronomia, Università di Firenze, and INFN, Sesto Fiorentino, 50019, Italy

    Giulio Pettini

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  1. Michele Modugno
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  3. Giulio Pettini
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Correspondence to Michele Modugno.

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Modugno, M., Ibañez-Azpiroz, J. & Pettini, G. Tight-binding models for ultracold atoms in optical lattices: general formulation and applications. Sci. China Phys. Mech. Astron. 59, 660001 (2016). https://doi.org/10.1007/s11433-015-0514-5

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