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Nonlinear Phenomena of Ultracold Atomic Gases in Optical Lattices: Emergence of Novel Features in Extended States

Center for Theoretical Physics of Complex Systems, Institute for Basic Science (IBS), Daejeon 34051, Korea
Department of Physics, Zhejiang University, Hangzhou 310027, China
University of Science and Technology (UST), Daejeon 34113, Korea
Asia Pacific Center for Theoretical Physics (APCTP), Pohang, Gyeongbuk 37673, Korea
Department of Physics, Pohang University of Science and Technology (POSTECH), Pohang, Gyeongbuk 37673, Korea
Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences, Innsbruck A-6020, Austria
Institute for Theoretical Physics, University of Innsbruck, Innsbruck A-6020, Austria
Department of Physics, University of Calcutta, Kolkata 700009, India
Authors to whom correspondence should be addressed.
Academic Editors: Ignazio Licata and Sauro Succi
Entropy 2016, 18(4), 118;
Received: 16 December 2015 / Revised: 5 March 2016 / Accepted: 17 March 2016 / Published: 31 March 2016
(This article belongs to the Special Issue Non-Linear Lattice)
PDF [1886 KB, uploaded 31 March 2016]


The system of a cold atomic gas in an optical lattice is governed by two factors: nonlinearity originating from the interparticle interaction, and the periodicity of the system set by the lattice. The high level of controllability associated with such an arrangement allows for the study of the competition and interplay between these two, and gives rise to a whole range of interesting and rich nonlinear effects. This review covers the basic idea and overview of such nonlinear phenomena, especially those corresponding to extended states. This includes “swallowtail” loop structures of the energy band, Bloch states with multiple periodicity, and those in “nonlinear lattices”, i.e., systems with the nonlinear interaction term itself being a periodic function in space. View Full-Text
Keywords: optical lattices; Bose–Einstein condensates; cold Fermi gases; superfluidity optical lattices; Bose–Einstein condensates; cold Fermi gases; superfluidity

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Watanabe, G.; Venkatesh, B.P.; Dasgupta, R. Nonlinear Phenomena of Ultracold Atomic Gases in Optical Lattices: Emergence of Novel Features in Extended States. Entropy 2016, 18, 118.

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