Ultra Cold Quantum Gases 2

III. BEC of the ideal gas
  13. Coherence properties
  14. Interference of condensates
IV. The weakly interacting BEC
  15. Cold collisions in dilute gases
  16. Gross-Pitaevskii equation
  17. Mean-field results for the atomic density
  18. Bogoliubov excitations
  19. Superfluidity
  20. Vortices
V. Strongly interacting systems
  21. Optical lattices
  22. Feshbach resonances and molecule association
  23. Fermions and BCS-BEC crossover

After successful completion of the module the students are able to:

• understand the basic properties of an ideal Bose-Einstein condensate
• apply models for the description of weak interactions in a condensate in various situations
• understand physical effects of ultracold gases in the strongly-interacting regime

Basic knowledge in quantum mechanics (PH0007), atomic physics (PH0016), electrodynamics (PH0006), and statistical physics (PH0008). Previous participation in „Ultracold quantum gases 1“ (PH2124) is helpful but not mandatory.

This module consists of a lecture and an exercise class.

In the thematically structured lecture the learning content is presented. With cross references between different topics, the concepts relevant for the covered topics are explained. In scientific discussions the students are involved to stimulate their analytic intellectual strength. Self-study of textbooks, review articles, and original literature, as e.g. referenced in the lectures notes provided, is an important part of the student’s learning process.

In the exercises the learning content is deepened using problem examples. Thus the students are able to apply and explain the learned physics knowledge independently.

PowerPoint, blackboard, lecture notes, tutorial sheets

• C.J. Pethick & H. Smith: Bose-Einstein condensation in dilute gases, Cambridge University Press, (2008)
• L. Pitaevskii & S. Stringari: Bose-Einstein Condensation, Clarendon Press, (2003)

There will be an oral exam of 25 minutes duration. Therein the achievement of the competencies given in section learning outcome is tested exemplarily at least to the given cognition level using comprehension questions and sample calculations.

For example an assignment in the exam might be:

• Where does the Gross-Pitaevskii equation come from?
• Which properties do quantized vortices in a BEC have?
• How does the quantum phase transition to the Mott insulator come about?

Participation in the exercise classes is strongly recommended since the exercises prepare for the problems of the exam and rehearse the specific competencies.