This book, written by experts in the fields of atomic physics and nonlinear science, covers the important developments in a special aspect of Bose-Einstein condensation, namely nonlinear phenomena in condensates. Topics covered include bright, dark, gap and multidimensional solitons; vortices; vortex lattices; optical lattices; multicomponent condensates; mathematical methods/rigorous results; and the beyond-the-mean-field approach.

Dilute-gas Bose-Einstein condensates offer a versatile testbed for the investigation of quantum phenomena. On the mean-field level, these ultracold atomic systems are described by the Gross-Pitaevskii equation which captures the nonlinearities induced by particle interactions. The analytical simplicity of behavior in the linear regime, i.e. in the absence of interparticle interactions, allows for the study of novel particle dispersions, generation of solid-state analogues, and the construction of atom interferometers. Nonlinearities lead to the formation of additional features such as solitonic matter-waves and dispersion loops.The first two studies in this dissertation investigate strongly nonlinear phenomena in 87Rb Bose-Einstein condensates. The inherently nonlinear matter-wave structures known as solitons have been previously realized in one- and two-component systems, Here, that work is extended to three-component systems where two new species of soliton are observed. The second study considers the effects of interactions in optical lattice systems. Nonlinear behavior in an optical lattice is generally avoided, especially in atom interferometry applications. When nonlinear behavior dominates over the optical lattice potential a novel band loop appears in the lowest band of the dispersion. In this dissertation, Rabi oscillations and Bloch oscillations are observed in condensates in weak optical lattices and the resultant non-adiabatic behavior is discussed.In the final two studies, novel quantum phases are generated by combining spin-orbit (SO) coupling with a second coupling type. For instance, supplementing the SO-coupling with optical lattice assisted hopping between the minima of the SO-coupled dispersion leads to the generation of the SO-coupled stripe phase. This phase is closely related to a supersolid, an exotic state of matter which simultaneously possesses the properties of a superfluid and a crystalline solid. By instead adding a radio-frequency field that also couples two Zeeman sublevels, an emergent lattice is formed which can exhibit Galilean invariant Kapitza-Dirac scattering and Bloch oscillations. Both of these compound coupling schemes are discussed.

Bose-Einstein condensation of excitons is a unique effect in which the electronic states of a solid can self-organize to acquire quantum phase coherence. The phenomenon is closely linked to Bose-Einstein condensation in other systems such as liquid helium and laser-cooled atomic gases. This is the first book to provide a comprehensive survey of this field, covering theoretical aspects as well as recent experimental work. After setting out the relevant basic physics of excitons, the authors discuss exciton-phonon interactions as well as the behaviour of biexcitons. They cover exciton phase transitions and give particular attention to nonlinear optical effects including the optical Stark effect and chaos in excitonic systems. The thermodynamics of equilibrium, quasi-equilibrium, and nonequilibrium systems are examined in detail. The authors interweave theoretical and experimental results throughout the book, and it will be of great interest to graduate students and researchers in semiconductor and superconductor physics, quantum optics, and atomic physics.

Covering general theoretical concepts and the research to date, this book demonstrates that Bose-Einstein condensation is a truly universal phenomenon.

This book is the second volume of lecture notes on various topics in nonlinear physics delivered by specialists in the field who gave courses in the small village of Peyresq (France) during summer schools (2000, 2001, 2002) organised by the Institut Non Linéaire de Nice (INLN), in collaboration with the Institut de Recherche de Physique Hors Equilibre (IRPHE). The goal is to provide good summaries on the state of the art of some domains in physics having the common denominator of belonging to nonlinear sciences, and to promote the transfer of knowledge between them.

"This book is the second volume of a compilation of lecture notes on various topics in nonlinear physics delivered by specialists during the summer schools organized by the Institut Non Linaeaire de Nice ... in Peyresq ... since 1998. The first volume, edited by R. Kaiser and J. Montaldi, contains courses from the years 1998 and 1999. This volume collects notes of the lectures given from the summers of 2000, 2001 and 2002"--Preface, v. 2.