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Quantum Physics with cold atoms and ions (2015)

Name of course: Quantum Physics with cold atoms and ions

ECTS credits: 5

Course parameters:
Language: English
Level of course: Master level or PhD
Time of year : Q4 2015
No. of hours: 6 hours per week. Either lectures or problem classes.
Capacity limits: None

Objectives of the course:

The participants will be introduced to the fascinating range of research topics in the field of cold atoms and ions. The course provides a thorough understanding of the various experimental techniques and the basic theoretical tools used in the field. The experimental and theoretical basis for describing cold quantum gases is explained, and we furthermore explore some of the new and hot research topics. The course enables the students to read research papers within the field.

Learning outcomes and competences:

At the end of the course, the student should be able to:

  • Describe the techniques to trap and cool neutral atoms and ions.
  • Explain the properties of small and large ion Coulomb crystals.
  • Discuss quantum optical experiments with ions.
  • Analyze quantum optical experiments with large Coulomb crystals.
  • Describe the low energy interaction between cold atoms.
  • Analyze the mean-field theory for Bose-Einstein condensation.
  • Describe the experimental realization of Bose-Einstein condensation.
  • Derive the Hubbard model as a description of atoms in optical lattices.
  • Discuss new experiments with Bose-Einstein condensates and optical lattices.

Course contents:

Techniques to trap and cool atoms in order to study and use their quantum mechanical properties are described. We focus both on techniques used for ions and for neutral atomic gases. Various quantum optical experiments with single or few ions will be analyzed including quantum jumps and sub-/super-radiation, as well as quantum logical units, which can be used for quantum computers. We will discuss Coulomb crystals formed by collections of ions at low temperatures. The scattering theory giving rise to the low energy effective interaction in neutral atomic gases is examined. We will then analyze Bose-Einstein condensation within a mean-field description, and we derive the so-called Gross-Pitaevskii equation. The experimental realization of this equation is explained and we discuss the elementary excitations of the condenstate using Bogoliubov theory. Finally, the Hubbard model is derived as an accurate description of atoms in optical lattices, and it is used to analyze experiments both in Aarhus and internationally.


 Quantum mechanics, Atomic and molecular physics I.

Name of lecturers:

Georg Bruun
Jan Arlt
Michael Drewsen

Type of course/teaching methods: 

Lectures and exercises


Notes and papers. The book ”Bose-Einstein Condensation in Dilute Gases” by C. Pethick og H. Smith is a useful reference.

Course homepage:

Course assessment:

30 minutes oral exam, 7-point grading scale. 


Department of Physics and Astronomy


1 April to 30 June 2015


Campus, 8000 Aarhus C


For registration:


If you have any questions, please contact Georg Bruun, email:

Comments on content: 
Revised 16.05.2017