Course Coordinator: 
Thomas Busch
Condensed Matter

This course explores a range of phenomena in advanced condensed matter and discusses their observation in synthetic quantum many body system consisting of ultracold atoms.  Topics include: quantum phase transitions, bosonic and fermionic Hubbard models, (artificial) gauge fields, low-dimensional systems, quantum spin models and applications in quantum computing and quantum simulation.

To introduce students to advanced ideas in quantum many body physics
Detailed Syllabus: 
  1. Quantum Phase Transitions
  2. Bloch States, Bloch Waves, Bloch Oscillations
  3. Optical Lattices
  4. Quantum Simulators
  5. Hubbard models (bosonic, fermionic, mixed)
  6. Bogoliubov Theory
  7. Numerical Methods
  8. Low dimensional systems, strong correlations, Bethe Ansatz
  9. Quantum Spin Systems
  10. High Tc Superconductors, BCS theory
  11. Artificial Gauge Fields (abelian and non-abelian)
  12. Quantum Hall Effect (integer and fractional)
  13. Quantum Information
  14. Measurement
Course Type: 
Homework: 50%, Project 25%, In-term tests, 25%.
Text Book: 
Ultracold Atoms in Optical Lattices: Simulating Quantum Many Body Systems, by Lewenstein, Sanpera, Ahufinger (2012) Oxford University Press
Reference Book: 
Quantum Theory of Solids, 2 edn, by Charles Kittel (1987) Wiley. Solid State Physics, 2 edn, by Ashcroft and Mermin (2002) Holt Rinehart & Winston