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Ultra-Cold Quantum Gases 2

Module PH7004

This module is offered by Ludwig-Maximilians University Munich (LMU). It is available for TUM students only within a joint degree program (e. g. M. Sc. Quantum Science & Technology).

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.

Basic Information

PH7004 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.

  • Focus Area Experimental Quantum Science & Technology in M.Sc. Quantum Science & Technology

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

Total workloadContact hoursCredits (ECTS)
270 h 90 h 9 CP

Responsible coordinator of the module PH7004 is Immanuel Bloch.

Content, Learning Outcome and Preconditions


This module covers advanced topics of ultracold quantum gas physics. Both the fundamental concepts and experimental work and concepts are described. Topics discussed include a detailed discussion of the physics of degenerate Fermi gases both with and without interactions. The interactions of quantum particles are explored, including Feshbach resonances and the unitary regime of Fermi gases, as well as Cooper pairing in the Bardeen-Cooper-Schrieffer (BCS) limit and the BEC-BCS crossover to the Bose Einstein condensate (BEC). Another section discusses interacting quantum gases in optical lattices, the Fermi-Hubbard model, quantum magnetism and lattice geometries beyond the square lattice. In addition, selected of modern areas of the quantum gas research field are discussed, such as for example synthetic gauge fields, low-dimensional quantum systems, long-range interactions, orbital quantum gases and quantum gas microscopy.

Learning Outcome

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

  1. Understand the physics of Fermi gases and apply related methods such as the Sommerfeld expansion.
  2. Discuss interacting Fermi gases and their quantum phase such as the BEC and the BCS limit.
  3. Explain various fundamental methods in quantum gas preparation, manipulation and detection of many-body states of the system.
  4. Describe the effects of quantum statistics on ultracold gases 5. Understand the effects of interactions on quantum gases with internal degree of freedom.


No preconditions in addition to the requirements for the general Master’s program in Physics, in particular no other quantum gas classes are required.

Courses, Learning and Teaching Methods and Literature

Learning and Teaching Methods

The module consists of a lecture and exercise classes. The main teaching material will typically be presented on the blackboard, supplemented by computer presentations to show / illustrate important results and discuss state-of-the-art research. 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. Furthermore, within the exercise classes original publications related to the module’s content are discussed.


Computer presentation, blackboard.


All literature on ultracold quantum gases, including review articles in scientific journals - 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) - Masahito Ueda: Fundamentals and new frontiers of Bose-Einstein condensation, World Scientific (2010) Starts with BEC, also includes advanced topics

Module Exam

Description of exams and course work

There will be a written exam of 120 minutes duration. Therein the achievement of the competencies given in section learning outcome is tested exemplarily at least to the given cognition level using calculation problems and comprehension questions.

For example an assignment in the exam might be:

  • Derivation of simple relationships and models such as the Sommerfeld approximation, or scattering phases
  • Explanation of phenomena such as superfluidity in fermionic gases
  • Discussion of the properties of the BEC-BCS crossover and derivation of related quantities
  • Calculation of simple few-particle models such as interactions and dynamics of particles in potential wells
  • Discussion of insulating and conductive behavior in lattices, and derivation of lattice properties such as band structures
  • Explanation and derivation of resonance phenomena in interacting particles

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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