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Ultra Cold Quantum Gases 2

Module PH2125

This module handbook serves to describe contents, learning outcome, methods and examination type as well as linking to current dates for courses and module examination in the respective sections.

Module version of SS 2022 (current)

There are historic module descriptions of this module. A module description is valid until replaced by a newer one.

Whether the module’s courses are offered during a specific semester is listed in the section Courses, Learning and Teaching Methods and Literature below.

available module versions
SS 2022SS 2020SS 2018SS 2011

Basic Information

PH2125 is a semester module in English language at Master’s level which is offered in summer semester.

This Module is included in the following catalogues within the study programs in physics.

  • Specific catalogue of special courses for condensed matter physics
  • Complementary catalogue of special courses for nuclear, particle, and astrophysics
  • Complementary catalogue of special courses for Biophysics
  • Complementary catalogue of special courses for Applied and Engineering Physics

If not stated otherwise for export to a non-physics program the student workload is given in the following table.

Total workloadContact hoursCredits (ECTS)
150 h 45 h 5 CP

Responsible coordinator of the module PH2125 is Stephan Dürr.

Content, Learning Outcome and Preconditions


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

Learning Outcome

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.

Courses, Learning and Teaching Methods and Literature

Courses and Schedule

VO 2 Ultra Cold Quantum Gases 2 Dürr, S. Wed, 12:00–14:00, PH II 227
UE 1 Exercise to Ultra Cold Quantum Gases 2 Stolz, T.
Responsible/Coordination: Dürr, S.
Tue, 12:00–14:00, PH-Cont. C.3201

Learning and Teaching Methods

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)

Module Exam

Description of exams and course work

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.

Exam Repetition

The exam may be repeated at the end of the semester.

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