University of Heidelberg

Tilman Enss | Teaching — Theory of Ultracold Atoms

as of 30 Mar 2021

Theory of Ultracold Atoms (MVSpec)

Summer term 2021

The field of ultracold atomic gases has undergone a remarkable development over the past few years and is now a key area of many-body physics at the interface to condensed matter, atomic and nuclear physics. This course introduces the theoretical concepts and methods of ultracold quantum gases and covers many timely examples, as seen in current experiments also in Heidelberg. Many of the topics that we discuss for cold atoms (Bose-Einstein condensation, superfluidity, fermion pairing, quantum phase transitions, thermalization) are at the same time more general paradigms of many-body physics and are used also in other areas of physics. The exercises also show how to compute experimental observables.


  1. Strongly interacting fermions: the BCS-BEC crossover
    • Scattering theory and Feshbach resonances
    • BCS theory of superconductivity
    • Bose-Einstein condensation and superfluidity
    • Unitary Fermi gas and scale invariance
    • Contact density and Tan relations
    • Fermi polarons and spectroscopy
  2. Bosons in optical lattices: the Mott Insulator—Superfluid transition
    • Optical lattices and Bose-Hubbard model
    • Mott Insulator—Superfluid transition
    • Quantum Critical Point, excitations and Higgs mode
    • Fermi-Hubbard model
    • Quantum Simulation
  3. Real-time dynamics and transport
    • Nonequilibrium dynamics and thermalization
    • Collective modes and transport
Lecture materials and homework problems (for participants)

Dates and Location

Lecture Tuesday and Thursday 09.15-11.00h, online [LSF].
Exercise Tuesday 14.15-16.00h, online.
Please register for the course to access lecture materials and for taking part in the exam; you may unregister yourself before June 30.


  • Quantum Mechanics (PTP4)
  • Theoretical Statistical Physics (MKTP1)
  • recommended: Advanced Quantum Theory (MVAMO2)


As an introduction, the lecture notes by Ketterle and Zwierlein are particularly recommended.

  • Ketterle and Zwierlein, Making, probing and understanding ultracold Fermi gases, Varenna lecture notes (2008).
  • Pitaevskii and Stringari, Bose-Einstein Condensation, Clarendon Press 2003.
  • Pethick and Smith, Bose-Einstein Condensation in Dilute Gases, Cambridge University Press 2008.
  • Zwerger (ed.), The BCS-BEC Crossover and the Unitary Fermi Gas, Springer Lecture Notes in Physics 836 (PDF available from the university library).
  • Diehl, Many-Body Physics with Cold Atoms, Innsbruck lecture notes (2013).
  • Bloch, Dalibard, and Zwerger, Many-body physics with ultracold gases, Rev. Mod. Phys. 80, 885 (2008).
  • Fetter and Walecka, Quantum Theory of Many-Particle Systems, Dover 2003.


The exam will be held on Thursday, 22 July 2021, from 09:00-11:00h.