Course Coordinator: 
Thomas Busch
Ultracold Quantum Gases

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.


The course introduces the students to the field of ultracold quantum gases. The lectures are combined with a weekly journal club, where original publications related to the lecture are discussed. Students will learn some fundamental concepts and techniques used in ultracold atoms research and obtain an overview over the many directions this diverse field is developing into. At the end of the course the students should be able to read current scientific literature and discuss work with researchers in the area. Since the area of ultracold quantum gases has connections to many other fields of physics, especially condensed matter and optics, students will be able to pick up aspects of these as well.
Course Content: 

1. Ultracold atomic gases: cooling and trapping

2. Bose-Einstein condensation and Fermi degeneracy in ideal gases

3. Interacting Bose-Einstein condensates: Gross-Pitaevskii equation.

4. Dynamics of Bose-Einstein condensates. Expanding and oscillating condensates.

5. Elementary excitations. Bogoliubov-De Gennes equations.

6. Two-dimensional Bose gases. Kosterlitz-Thouless transition.

7. Vortices and Superfluidity

8. One-dimensional systems: quasi-condensates and solitons

9. Strongly interacting 1D Bose gases. Impenetrable bosons.

10. Degenerate Fermi gases: BEC and BCS transitions

11. Optical lattices

12. Artificial Gauge fields

13. Applications in quantum information and metrology

Course Type: 
Homework: 50%, Project 25%, In-term tests, 25%.
Text Book: 
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
Reference Book: 
Modern Quantum Mechanics, by J. J. Sakurai (1994) Addison-Wesley
Quantum Mechanics, by J.-L. Basdevant and J. Dalibard (2002) Springer
Prior Knowledge: 

While the fundamental concepts of atomic physics and quantum mechanics that are required will be reviewed in the beginning of the course, basic prior knowledge of quantum mechanics is required (e.g. undergraduate quantum mechanics).

Companion course to A211 Advances in Atomic Physics