Ultracold Atomic Quantum Gases

Lecture

Thomas Gasenzer & Markus Oberthaler

Wednesday, 09:15-11:00, INF 227 SR 1.403 Süd, & Friday, 15:15-17:00, SR Pw 19 [LSF]

Content of the theory part:

• Ideal gases: Bose-Einstein & Fermi-Dirac, uniform & trapped
• Introduction to alkali atoms and their interactions at low energies
  - Atomic structure - Born-Oppenheimer potentials - Low-energy scattering theory - Many-body Hamiltonian, energy functional & stationary ground state
• Many-body theory of a BEC
  - Gross-Pitaevskii equation - Hydrodynamic interpretation - Elementary & collective excitations - Fock space formulation - Hartree-Fock-Bogoliubov theory - Finite temperature - Quantum effects (damping, ...)
• Low-dimensional gases
  - 1D Bose gas: interaction parameter, - Lieb-Liniger, Tonks-Girardeau - 2D Bose gas: interactions - KT transition
• Lattices
  - Bloch wave functions, Wannier basis, Bose-Hubbard - Mott insulator (perturbation theory) - Mean-field theory - (Gutzwiller, DMRG, ...)
• Coherence
  - Two-mode model - phase and number distributions - number states vs. coherent states - 1st vs. 2nd order coherence - Squeezing
• Strongly interacting systems
  - Interactions with the radiation field, (Bragg diffraction) - Scattering resonances (Feshbach, Photoassociation) (- Dynamical HFB) (- A glimpse on theory for strong interactions)
• Degenerate Fermi-gases
  - Interactions - Mean-field theory, ground state, excitations, finite temperature - Pairing - BEC-BCS

Prerequisites:

• Quantum Mechanics (Theoretical Physics III), Statistical Mechanics (Theor. Phys. IV) would be helpful

Literature:

• K. Huang, "Statistical Mechanics", Wiley (1987).
• C.J. Pethick and H. Smith, "Bose-Einstein condensation in Dilute Gases, CUP, Cambridge (2002).
• A. Leggett, "Bose-Einstein condensation in the alkali gases: Some fundamental concepts", Review of Modern Physics 73, 307 (2001)
  (Full text as pdf available through UB proxy server).
• L.P. Pitaevskii and S. Stringari, "Bose-Einstein condensation", Clarendon Press, Oxford (2003).
• F. Dalfovo, S. Giorgini, L. P. Pitaevskii, and S. Stringari, "Theory of Bose-Einstein condensation in trapped gases", Review of Modern Physics 71, 463 (1999).
  (Full text as pdf available through UB proxy server).