Emergent Nonlinear Phenomena in Bose-Einstein Condensates

1. Front Matter

   Pages I-XXII

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2. Basic Mean-Field Theory for Bose-Einstein Condensates

   1. Basic Mean-Field Theory for Bose-Einstein Condensates

      • P. G. Kevrekidis, D. J. Frantzeskakis, R. Carretero-González

      Pages 3-21

3. Bright Solitons in Bose-Einstein Condensates

   1. Bright Solitons in Bose-Einstein Condensates: Theory

      • F. Kh. Abdullaev, J. Garnier

      Pages 25-43

   2. Bright Solitons: Summary of Experimental Techniques

      • L. Khaykovich

      Pages 45-61

4. Dark Solitons in Bose-Einstein Condensates

   1. Dark Solitons in Bose-Einstein Condensates: Theory

      • V. V. Konotop

      Pages 65-83

   2. Dark Solitons in BECs: The First Experiments

      • B. P. Anderson

      Pages 85-96

5. Nonlinear Localization of BECs in Optical Lattices

   1. Nonlinear Localization of BECs in Optical Lattices

      • E. A. Ostrovskaya, M. K. Oberthaler, Y. S. Kivshar

      Pages 99-130

6. Multi-Dimensional Solitons in Bose-Einstein Condensates

   1. Multidimensional Solitons: Theory

      • L. D. Carr, J. Brand

      Pages 133-156

   2. Experiments on Multidimensional Solitons

      • J. Brand, L. D. Carr, B. P. Anderson

      Pages 157-169

7. Vortices in Bose-Einstein Condensates

   1. Vortices in Bose-Einstein Condensates: Theory

      • N. G. Parker, B. Jackson, A. M. Martin, C. S. Adams

      Pages 173-189

   2. Vortices in Bose-Einstein Condensates: Experiments

      • F. Chevy

      Pages 191-207

8. Vortex Lattices

   1. Vortex Lattices in Bose-Einstein Condensates: Theory

      • M. Ueda, H. Saito

      Pages 211-228

   2. Vortex Lattices in Bose-Einstein Condensates: Experiments

      • C. Raman

      Pages 229-243

9. Optical Lattices

   1. Optical Lattices: Theory

      • A. Smerzi, A. Trombettoni

      Pages 247-265

   2. Bose-Einstein Condensates in Optical Lattices: Experiments

      • O. Morsch

      Pages 267-283

10. Multi-Component Bose-Einstein Condensates

    1. Multi-Component Bose-Einstein Condensates: Theory

       • B. Malomed

       Pages 287-305

    2. Multi-Component Condensates: Experiment

       • D. S. Hall

       Pages 307-327

11. Manipulations of Coherent Matter-Waves

    1. Manipulations of Coherent Matter-Waves

       • P. G. Kevrekidis, D. J. Frantzeskakis, R. Carretero-González

       Pages 331-349

12. Beyond Gross-Pitaevskii Mean Field Theory

    1. Beyond Gross-Pitaevskii Mean-Field Theory

       • N. P. Proukakis

       Pages 353-373

13. Asymptotic Reductions of the Gross-Pitaevskii Equation

    1. Asymptotic Reductions of the Gross-Pitaevskii Equation

       • D. E. Pelinovsky

       Pages 377-398

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.

• Atomic physics
• BEC
• Nonlinear science
• experiment
• vortices
• fluid- and aerodynamics

• University of Massachusetts, Amherst, USA

  Panayotis G. Kevrekidis

• University of Athens, Athens, Greece

  Dimitri J. Frantzeskakis

• San Diego State University, San Diego, USA

  Ricardo Carretero-González

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.

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