Frontiers of Quantum Gas Research: Few- and Many-Body Physics

Prof. Cheng Chin, James Franck institute, Enrico Fermi institute, and Department of Physics, University of Chicago
Prof. Sebastian Huber, ETHZ.

Where: HIT J52
When: Tue 08:45-11:45 (V+U)

General remarks on the exercise class

Problem sets will be handed out on Tuesdays during the lecture (not during the first week), and are to be handed in before the next Monday at 12:00. Your solutions may be handed in via the mailboxes next to the secretaries on the K-floor of the HIT building. Please put them in the mailbox of Evert van Nieuwenburg.

Note: Please clearly indicate on your solution sheets which exercises you want to have explicitly checked, if you find that the exercise class and solution sheet are not enough. Handing in your solutions will be noticed irrespective of whether you want them to be checked or not.

  1. Lecture 01: 18.02: Introduction/Degenerate Fermi gase ( pdf )
  2. Lecture 02: 25.02: Superconductivity, BCS theory, superfluidity ( pdf,iPy)
  3. Lecture 03: 04.03: Topological superfluids ( pdf,iPy and Chern module)
  4. Lecture 04: 11.03: First experiments on strongly interacting Fermi gases ( pdf )
  5. Lecture 05: 18.03: Molecular BEC and BEC-BCS crossover ( pdf )
  6. Lecture 06: 25.03: Efimov physics ( pdf )
  7. Lecture 07: 01.04: Fermi Hubbard model ( pdf )
  8. Lecture 08: 08.04: Quantum magnetism ( pdf )
  9. Lecture 09: 15.04: Quantum phase transitions I ( pdf )
  10. Lecture 10: 29.04: Quantum phase transitions II ( pdf )
  11. Lecture 11: 06.04: Non-equiulibrium phase transitions I, examples ( pdf )
  12. Lecture 12: 13.04: Non-equiulibrium phase transitions II, Master equation ( pdf )
  13. Lecture 13: 20.04: Non-equiulibrium phase transitions III

Paper references for the paper discussions

  1. De Marco and Jin, Onset of Fermi Degeneracy in a Trapped Atomic Gas, Science, 285, 1703 (1999).
  2. Chin et al., Observation of the Pairing Gap in a Strongly Interacting Fermi Gas, Science, 305, 5687 (2004).
  3. Bühler et al. Majorana modes and p-wave superfluids for fermionic atoms in optical lattices, arXiv:1403.0593 (2014).

Exercises

  1. Problem Set 1
  2. Fill in the steps in the mean-field calculation of the BCS theory (see lecture notes).
  3. Implement the tt’-model, and investigate the edge states. You can start from the example file: 1D.py
  4. Problem Set 4
  5. Problem Set 5
  6. Problem Set 7
  7. Problem Set 8
  8. Problem Set 11 and example code: chipping.py
  9. Problem Set 12 (updated since handout!)

Literature

You will find a list of useful literature below. The list might be updated during the course of the lecture.

  1. Stefano Giorgini, Lev P. Pitaevskii, and Sandro Stringari, Theory of ultracold atomic Fermi gases, Rev. Mod. Phys. 80, 1215 (2008)
  2. N. Ashcroft and N. Mermin, Solid state physics, Harcourt, (1987).
  3. A. Auerbach, Interacting electrons and Quantum Magnetism, Springer (1994).
  4. C.W. Gardiner and P. Zoller, Quantum Noise, Springer (2000).