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Cold Bosonic Atoms in Optical Lattices

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TLDR
In this paper, the Bose-Hubbard model was used to model the phase transition from the superfluid to the Mott insulator phase induced by varying the depth of the optical potential.
Abstract
The dynamics of an ultracold dilute gas of bosonic atoms in an optical lattice can be described by a Bose-Hubbard model where the system parameters are controlled by laser light We study the continuous (zero temperature) quantum phase transition from the superfluid to the Mott insulator phase induced by varying the depth of the optical potential, where the Mott insulator phase corresponds to a commensurate filling of the lattice (``optical crystal'') Examples for formation of Mott structures in optical lattices with a superimposed harmonic trap and in optical superlattices are presented

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Journal ArticleDOI

Many-Body Physics with Ultracold Gases

TL;DR: In this article, a review of recent experimental and theoretical progress concerning many-body phenomena in dilute, ultracold gases is presented, focusing on effects beyond standard weakcoupling descriptions, such as the Mott-Hubbard transition in optical lattices, strongly interacting gases in one and two dimensions, or lowest-Landau-level physics in quasi-two-dimensional gases in fast rotation.
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Quantum Phase Transition From a Superfluid to a Mott Insulator in a Gas of Ultracold Atoms

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Maximally-localized Wannier Functions: Theory and Applications

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Quantum Simulation

TL;DR: The main theoretical and experimental aspects of quantum simulation have been discussed in this article, and some of the challenges and promises of this fast-growing field have also been highlighted in this review.
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Quantum simulations with ultracold quantum gases

TL;DR: In this paper, a review of advances in this field is presented and discussed the possibilities offered by this approach to quantum simulation, as well as the possibilities of quantum simulation with ultracold quantum gases.
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