Ultra-Cold Quantum Gases 1

This module gives an introduction to ultracold quantum gas physics. It covers both the underlying concepts and describes modern experiments in the field. It starts with fundamental concepts such as quantum statistics, the thermodynamics of quantum gases and Bose condensation and with basic methods such cooling, trapping and detection of quantum gases, with an emphasis on ultracold Bose gases. A main focus of ultracold quantum gas physics is the description of interacting systems, which is introduced by deriving and discussing low energy scattering processes, and then the physics of interacting Bose gases. Here fundamental theories such as the Gross-Pitaevskii and Thomas Fermi regimes are derived and discussed. Resulting phenomena such as superfluidity, solitons, and rotation in quantum gases are discussed. Another section is devoted to the physics of quantum gases in periodic potentials, to access the physics of strongly interacting quantum system phenomena such as the superfluid-to-Mott insulator transition.

After completing the Module the student is able to:

1. Use quantum mechanics to describe gases and understand effects such as Bose condensation.

2. Describe and explain phenomena in Bose gases with interactions such as superfluidity or solitons.

3. Explain various fundamental methods in quantum gas preparation, manipulation and detection.

4. Describe the role of coherence in Bose gases.

5. Understand the basic physics of interacting atoms in periodic potentials.

No prerequisites beyond the requirements for the Master’s program in Quantum Science and Technology.

The module consists of a lecture series (4 SWS) and exercise classes (2 SWS), comprising two lecture sessions and one exercise session per week. 

The main teaching material will typically be presented on the blackboard, supplemented by computer presentations to show important results and to discuss current ongoing research. As part of the lecture there will be a weekly Journal Club, where original publications related to the module’s content are discussed. Weekly problem sets are offered to obtain a better comprehension of the lecture content and to improve their familiarity with them. The solutions to the problem sets are discussed in the weekly exercise classes.

Participation in the exercise classes is strongly recommended since they strongly support understanding of the material from the lecture, and help prepare for learning the knowledge and techniques expected in the exam.

Computer presentation, blackboard

There are a few textbooks on some of the topics discussed in this class:

• Christopher J. Foot: Atomic Physics, Oxford University Press (2005): Introductory text including fundamental atomic physics topics

• C.J. Pethick and H. Smith: Bose-Einstein Condensation in Dilute Gases, Cambridge University Press (2002)

• H. Metcalf and P. van der Straten: Laser cooling and trapping, Springer (1999)
   Specifically covers laser cooling

• Masahito Ueda: Fundamentals and new frontiers of Bose-Einstein condensation, World Scientific (2010): Starts with BEC, also includes advanced topics

There will be an oral exam of 30 minutes duration. Therein the achievement of the competencies given in section learning outcome is tested exemplarily at least to the given cognition level using conceptual questions and computational tasks.

For example an assignment in the exam might be:

• Explanation and discussion of Bose condensation
• Derivation of simple models of interacting quantum ases such as Gross-Pitaevskii or Thomas-Fermi
• Explanation and discussion of superfluidity-related phenomena, such as the occurrence of solitons or special properties of quantum gases with angular momentum
• Discussion of the motion of ultracold particles in lattice potenials
• Explanation and discussion of methods for manipulation and cooling o quantum gases