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Ultracold Atoms in Optical LatticesSimulating quantum many-body systems$
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Maciej Lewenstein, Anna Sanpera, and Verònica Ahufinger

Print publication date: 2012

Print ISBN-13: 9780199573127

Published to Oxford Scholarship Online: December 2013

DOI: 10.1093/acprof:oso/9780199573127.001.0001

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Ultracold gases in optical lattices: basic concepts

Ultracold gases in optical lattices: basic concepts

(p.36) 3 Ultracold gases in optical lattices: basic concepts
Ultracold Atoms in Optical Lattices

Maciej Lewenstein

Anna Sanpera

Verònica Ahufinger

Oxford University Press

This chapter describes basic methods to realise optical potentials and optical lattices, listing in detail what can be controlled in ultracold atomic systems. It revisits the properties of non-interacting particles in periodic lattices: band structure, Bloch functions, and Wannier states. The chapter derives the Hubbard model in the tight binding approximation, and discusses Bose–Einstein condensates in optical lattices in a weak interacting limit, and in a strongly correlated regime.

Keywords:   optical potentials, optical lattices, band structure, Bloch functions, Wannier states, Hubbard model, tight binding approximation, Bose-Einstein condensates, weak interacting limit, strongly correlated regime

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