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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

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

Maciej Lewenstein

Anna Sanpera

Verònica Ahufinger

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199573127.003.0003

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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