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This book offers a detailed introduction to Bose-Einstein condensates (BECs) and nonlinear quantum systems, tailored for advanced undergraduates and researchers. It bridges foundational concepts with modern developments in quantum condensed matter. Starting with the history and experimental milestones of BECs, it explores theoretical models including mean-field and beyond-mean-field approaches for both scalar and vectorial condensates. Analytical techniques such as inverse scattering and soliton theory are covered alongside numerical methods for solving the Gross-Pitaevskii equation. Applications span optical solitons, quantum vortices, and exciton-polariton physics. Each topic is supported by examples, problem sets, and computational tools, equipping readers with both theoretical insight and practical skills to engage with cutting-edge research areas like quantum turbulence and supersolids.
Key features:
- Introduces the subject at the very basic level
- Includes the analytical and theoretical methods
- Contains numerical methods
- Provides worked examples, end-of-chapter summaries, and homework problems
Chapter 1. Introduction
Chapter 2. Analytical methods
Chapter 3. Numerical techniques
Chapter 4. Bose–Einstein condensates and optical solitons
Chapter 5. Dynamics of scalar Bose–Einstein condensates with short-range interactions
Chapter 6. Vectorial condensates
Chapter 7. Spin–orbit-coupled Bose–Einstein condensates
Chapter 8. Bose–Einstein condensates with long-range interactions
Chapter 9. Collisionally inhomogenous Bose–Einstein condensates
Chapter 10. Quantum vortices in Bose–Einstein condensates
Chapter 11. Nascent outlook of exciton–polariton condensates
Chapter 12. Roadmap ahead