Quantum Optics and Ultracold Atoms

Prof. Dr. Giovanna Morigi

Vorlesung

  • Mittwoch 16:00 - 18:00 Uhr, Gebäude E2 6, Raum 1.06
  • Donnerstag 16:00 - 18:00 Uhr, Gebäude E2 6, Raum 1.06

Vorlesungsbeginn: Mittwoch, 06. November.

Material zur Vorbereitung wird zu einem späteren Zeitpunkt hier hochgeladen.

Content

  1. Bose-Einstein statistics and condensation:
    The ideal Bose gas: Thermodynamics and Statistics
     
  2. Quantum degenerate atomic gases
    2.1 Trapping and cooling
    2.2 Collisions
     
  3. 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
     
  4. Second quantization
    4.1 The Schroedinger equation in first quantization
    4.2 Many-particle Hilbert space
    4.3 Fields
     
  5. 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
     
  6. Superfluidity
    6.1 Landau’s criterion
    6.2 BEC and superfluidity
    6.3 Hydrodynamic theory of superfluids at zero temperature
    6.4 Quantum hydrodynamics
     
  7. BEC and coherence: Interference between two condensates
     
  8. 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
     
  9. Outlook: Ultracold Fermi gases, BEC/BCS transition, quantum simulators with ultracold atoms.

Literature

  • A. J. Leggett, Quantum Liquids
  • L. Pitaevskii, S. Stringari, Bose-Einstein Condensation
  • C. J. Pethick andH. Smith, Bose-Einstein Condensation in Dilute Gases
  • S. Sachdev, Quantum Phase Transitions
  • K. Huang, Statistical Mechanics
  • A. L. Fetter and J. D. Walecka, Quantum theory of many-particle systems