Emergent Nonlinear Phenomena in Bose-Einstein Condensates Theory and Experiment

The ?eld of Bose–Einstein condensation in atomic gases has been full of s- prises.Whathappenedafterthe?rstrealization ofBose–Einstein condensates in 1995 has far exceeded the vision of their creators. Originally, I expected interesting studies of equilibrium properties and dynamics, but the Bose– Einstein condensate became a pristine platform for a host of scienti?c studies. The condensate turned out to be a well-controlled medium for nonlinear wave phenomenaincludingfour-wavemixing,darkandbrightsolitons,anddynamic instabilities. Rotating condensates gave access to the rich physics of vortices and vortex lattices. The availability of di?erent hyper?ne states led to mul- component or spinor condensates, and optical lattices opened up yet another major frontier which is still rapidly expanding. Feshbach resonances and c- densation of fermion pairs will provide interesting phenomena to study for many more years to come. This rapid development of the ?eld has been fueled by a unique int- play between experiment and theory. Although experimentalists had the lead in realizing new systems, many phenomena were ?rst predicted and then observed. The present book re?ects this symbiosis by a balance of theoretical and experimental contributions. Twelve years after its beginning, the ?eld has reached a degree of maturity which is much better represented by a comp- hensive book than by a collection of original articles. I therefore expect this book not only to provide a valuable introduction to many young researchers who are joining this ?eld, but also serve as a reference for further studies of nonlinear phenomena in this rich system.

Basic Mean-Field Theory for Bose-Einstein Condensates.- Basic Mean-Field Theory for Bose-Einstein Condensates.- Bright Solitons in Bose-Einstein Condensates.- Bright Solitons in Bose-Einstein Condensates: Theory.- Bright Solitons: Summary of Experimental Techniques.- Dark Solitons in Bose-Einstein Condensates.- Dark Solitons in Bose-Einstein Condensates: Theory.- Dark Solitons in BECs: The First Experiments.- Nonlinear Localization of BECs in Optical Lattices.- Nonlinear Localization of BECs in Optical Lattices.- Multi-Dimensional Solitons in Bose-Einstein Condensates.- Multidimensional Solitons: Theory.- Experiments on Multidimensional Solitons.- Vortices in Bose-Einstein Condensates.- Vortices in Bose-Einstein Condensates: Theory.- Vortices in Bose-Einstein Condensates: Experiments.- Vortex Lattices.- Vortex Lattices in Bose-Einstein Condensates: Theory.- Vortex Lattices in Bose-Einstein Condensates: Experiments.- Optical Lattices.- Optical Lattices: Theory.- Bose-Einstein Condensates in Optical Lattices: Experiments.- Multi-Component Bose-Einstein Condensates.- Multi-Component Bose-Einstein Condensates: Theory.- Multi-Component Condensates: Experiment.- Manipulations of Coherent Matter-Waves.- Manipulations of Coherent Matter-Waves.- Beyond Gross-Pitaevskii Mean Field Theory.- Beyond Gross-Pitaevskii Mean-Field Theory.- Asymptotic Reductions of the Gross-Pitaevskii Equation.- Asymptotic Reductions of the Gross-Pitaevskii Equation.

Panayotis G. Kevrekidis received a B.S. in Physics from University of Athens, an M.S., M.Phil and Ph.D in Physics from Rutgers University. After a post-doctoral year between Princeton University and Los Alamos National Lab, he joined the department of Mathematics and Statistics of UMass, Amherst where he is currently an Associate Professor. He has published more than 150 research papers and has received a CAREER award in Applied Mathematics from the U.S. National Science Foundation.

Dimitri J. Frantzeskakis received a Diploma from University of Patras and a PhD Degree from National Technical University of Athens (NTUA), both in Electrical Engineering. After a postdoctoral year at NTUA, he joined the Department of Physics of University of Athens, where he is currently an Associate Professor. His research interests are focused on the dynamics of nonlinear waves and solitons with applications to various physical problems. He has published some 100 research papers.

Ricardo Carretero-González received a summa-cum-laude B.S. in Physics from Universidad Nacional Autónoma de México, a MPhil/PhD from Queen Mary, University of London. After a couple of postdocs at University College London and Simon Fraser University, he joined the department of Mathematics and Statistics at San Diego State University where he is currently Associate Professor and co-director of the Nonlinear Dynamical Systems group. He has published some 50 research papers.