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

被引:7
作者
Modugno, Michele [1 ,2 ]
Ibanez-Azpiroz, Julen [3 ,4 ,5 ]
Pettini, Giulio [6 ,7 ]
机构
[1] Univ Basque Country, UPV EHU, Dept Fis Teor & Hist Ciencia, E-48080 Bilbao, Spain
[2] Basque Fdn Sci, Ikerbasque, Bilbao 48011, Spain
[3] Forschungszentrum Julich, Peter Grunberg Inst, D-52425 Julich, Germany
[4] Forschungszentrum Julich, Inst Adv Simulat, D-52425 Julich, Germany
[5] JARA, D-52425 Julich, Germany
[6] Univ Florence, Dipartimento Fis & Astron, I-50019 Sesto Fiorentino, Italy
[7] INFN, I-50019 Sesto Fiorentino, Italy
来源
SCIENCE CHINA-PHYSICS MECHANICS & ASTRONOMY | 2016年 / 59卷 / 06期
关键词
ultracold atoms; optical lattices; tight-binding models; Wannier functions; effective Dirac equation; honeycomb lattices; WANNIER FUNCTIONS; DIRAC POINTS; MAGNETIC-FIELD; ENERGY; ELECTRONS; LOCALIZATION; DIAMAGNETISM; REALIZATION; GASES;
D O I
10.1007/s11433-015-0514-5
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
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.
引用
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页数:23
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