Optical Lattices: Theory

Abstract

This chapter presents an overview of the properties of a Bose-Einstein condensate (BEC) trapped in a periodic potential. This system has attracted a wide interest in the last years, and a few excellent reviews of the field have already appeared in the literature (see, for instance, [1-3] and references therein). For this reason, and because of the huge amount of published results, we do not pretend here to be comprehensive, but we will be content to provide a flavor of the richness of this subject, together with some useful references. On the other hand, there are good reasons for our effort. Probably, the most significant is that BEC in periodic potentials is a truly interdisciplinary problem, with obvious connections with electrons in crystal lattices, polarons and photons in optical fibers. Moreover, the BEC experimentalists have reached such a high level of accuracy to create in the lab, so to speak, paradigmatic Hamiltonians, which were first introduced as idealized theoretical models to study, among others, dynamical instabilities or quantum phase transitions.

Chapter 13 in Part VIII: "Optical Lattices" of "Emergent Nonlinear Phenomena in Bose-Einstein Condensates: Theory and Experiment," edited by P. G. Kevrekidis, D. J. Frantzeskakis, and R. Carretero-Gonzalez (Springer Series on Atomic, Optical, and Plasma Physics, 2007) - pages 247-265

References in corpus (16)

• Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms
• Direct Observation of Tunneling and Nonlinear Self-Trapping in a single Bosonic Josephson Junction
• The cold atom Hubbard toolbox
• Matter-wave interferometry in a double well on an atom chip
• A Bose-Einstein condensate in a random potential
• Suppression of Transport of an Interacting Elongated Bose-Einstein Condensate in a Random Potential
• Superfluidity of Bose-Einstein Condensate in An Optical Lattice: Landau-Zener Tunneling and Dynamical Instability
• Nonlinear Self-Trapping of Matter Waves in Periodic Potentials
• The Gross-Pitaevskii Equation for Bose Particles in a Double Well Potential: Two Mode Models and Beyond
• Routes towards Anderson-Like localization of Bose-Einstein condensates in disordered optical lattices
• Interference of an array of independent Bose-Einstein condensates
• Bose-Einstein condensates in 1D optical lattices: compressibility, Bloch bands and elementary excitations
• Parametric excitation of a Bose-Einstein condensate in a 1D optical lattice
• Beyond the Landau Criterion for Superfluidity
• Bogoliubov speed of sound for a dilute Bose-Einstein condensate in a 3d optical lattice
• Velocity of sound in a Bose-Einstein condensate in the presence of an optical lattice and transverse confinement