The course will start out by introducing the fundamental ideas for cooling and trapping ultracold atoms and review the quantum mechanical framework that underlies the description of interacting matter waves in the ultracold regime. This will introduce the idea of degenerate Bose and Fermi gases, and in particular the concept of Bose-Einstein condensation.
After this the main properties of Bose-Einstein condensates will be discussed, including coherence and superfluidity, and for Fermi gases the physics of the BCS transition will be introduced. Conceptually important developments such as optical lattices, Feshbach resonances, artificial gauge fields and others will be explained in detail as well. New developments in the area of strongly correlated gases will be introduced and applications of cold atoms in quantum information or quantum metrology provide the final part of the course.
The course will mostly focus on the theoretical description of ultracold quantum gases, but regularly discuss experimental developments, which go with these.
- Ultracold atomic gases: cooling and trapping
- Bose-Einstein condensation and Fermi degeneracy in ideal gases
- Interacting Bose-Einstein condensates: Gross-Pitaevskii equation.
- Dynamics of Bose-Einstein condensates. Expanding and oscillating condensates.
- Elementary excitations. Bogoliubov-De Gennes equations.
- Two-dimensional Bose gases. Kosterlitz-Thouless transition.
- Vortices and Superfluidity
- One-dimensional systems: quasi-condensates and solitons
- Strongly interacting 1D Bose gases. Impenetrable bosons.
- Degenerate Fermi gases: BEC and BCS transitions
- Optical lattices
- Artificial Gauge fields
- Applications in quantum information and metrology
- Bose-Einstein Condensation in Dilute Gases C.J. Pethick and H. Smith (2002) Cambridge University Press
- Bose-Einstein Condensation L.P. Pitaevskii and S. Stringari (2003) Oxford University Press
- Fundamentals and New Frontiers of Bose--Einstein Condensation M. Ueda (2010) World Scientific
- Modern Quantum Mechanics, by J. J. Sakurai (1994) Addison-Wesley
- Quantum Mechanics, by J.-L. Basdevant and J. Dalibard (2002) Springer
Alternate years course: next run in AY2023 and AY2025