Quantum Optics with Ultracold Atoms (Optional Course)

Lecturer: Giovanna Morigi
Exercises and tutorium: Thomas Fogarty

Thursday 12:30 - 14:00 Uhr, Gebäude E2 6, E.04
Friday 8:30 - 10:00 Uhr, Gebäude E2 6, Seminarraum 4.18

The first lecture takes place on Thursday, October 22 at 8.30am in Geb. E2.6, Seminar Room 4.18.

Rescheduled date: there is a lecture on Tuesday, January 26, at 14:00 in building E2.6 in room E12.

Bose-Einstein statistics and condensation:
The ideal Bose gas: Thermodynamics and Statistics
Quantum degenerate atomic gases
2.1 Trapping and cooling
2.2 Collisions
Bose-Einstein condensation in interacting systems
3.1 Definition of Bose-Einstein condensation in an interacting system
3.2 An imperfect Bose gas
3.3 Order parameter
Second quantization
4.1 The Schroedinger equation in first quantization
4.2 Many-particle Hilbert space
4.3 Fields
Bose-Einstein condensation in second quantization
5.1 Bogoliubov approximation
5.2 The Gross-Pitaevskii equation
5.3 Small amplitude oscillations
5.4 Quantization of elementary oscillations
Superfluidity
6.1 Landau’s criterion
6.2 BEC and superfluidity
6.3 Hydrodynamic theory of superfluids at zero temperature
6.4 Quantum hydrodynamics
BEC and coherence: Interference between two condensates
BEC in optical lattices
8.1 One particle in a periodic potential
8.2 Wannier functions
8.3 Equilibrium properties of BEC in optical lattices
8.4 Bose-Hubbard model, the Mott-insulator/Superfluid quantum phase transition
Outlook: Ultracold Fermi gases, BEC/BCS transition, quantum simulators with ultracold atoms.