Quantum Optics with Ultracold Atoms (Optional Course)

Lecturer: Giovanna Morigi
Exercises and tutorium: Thomas Fogarty

Lecture:

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.

Content

  1. Bose-Einstein statistics and condensation:
    The ideal Bose gas: Thermodynamics and Statistics

  1. Quantum degenerate atomic gases
    2.1 Trapping and cooling
    2.2 Collisions

  1. 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

  1. Second quantization
    4.1 The Schroedinger equation in first quantization
    4.2 Many-particle Hilbert space
    4.3 Fields

  1. 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

  1. Superfluidity
    6.1 Landau’s criterion
    6.2 BEC and superfluidity
    6.3 Hydrodynamic theory of superfluids at zero temperature
    6.4 Quantum hydrodynamics

  1. BEC and coherence: Interference between two condensates

  1. 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

  1. 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