University of Heidelberg

Tilman Enss | Teaching — Theory of ultracold atoms

as of 16 Sept 2016

News


2016-09-16: Seminar topics online.

Theory of ultracold atoms (MVSeminar)

Winter term 2016/17


This theory seminar introduces key questions and concepts in the fast-evolving field of ultracold atomic gases.
Supervisor: Priv.-Doz. Dr. Tilman Enss
general objectives of advanced mandatory seminars (page 18)
Fri 9.15-11.00h, Philosophenweg 19, SR [LSF]
First meeting: Friday Oct. 21, assignment of topics.

Interested? Please let me know by email.

Seminar Topics

  1. Scattering of ultracold atoms and Feshbach resonances [intro]
    low-energy scattering can be characterized by an s-wave scattering length, which diverges at a Feshbach resonance, leading to strong interactions; this is described by single- and two-channel models
    Ketterle, ch. 4.1-4.2, parts of 5; Bloch/Dalibard/Zwerger, ch. I
  2. Bose-Einstein condensates and Bogoliubov theory
    many bosons can condense into a single quantum state to form a BEC; excitations in the BEC are described by Bogoliubov theory
    Pitaevskii, ch. 2, 4, 6.1-6.2
  3. Vortices in rotating Bose-Einstein condensates
    the dynamics of a BEC can be described by the Gross-Pitaevskii equation, which admits vortex solutions in a rotating BEC
    Pitaevskii, ch. 5
  4. Bose-Hubbard model and the Mott insulator transition
    with bosonic atoms in an optical lattice one can realize a Bose-Hubbard model, which exhibits a phase transition between a Mott insulator and a superfluid state
    Bloch/Dalibard/Zwerger, ch. IV; Diehl p. 138-172 (in particular 148-160, 168-172); (Jaksch)
  5. The BCS-BEC crossover
    the interacting Fermi gas exhibits a smooth crossover from a weakly attractive BCS superfluid through the strongly interacting unitary regime to a weakly repulsive Bose-Einstein condensate of molecules
    Zwerger, ch. 3 (by Heiselberg); Ketterle, ch. 4.3++; Bloch/Dalibard/Zwerger, ch. VIII
  6. Fermi polarons
    a mobile impurity in a Fermi gas will travel through the gas at weak interaction, but can bind into a molecule at strong attraction; if interactions are switched on quickly, the new state may even become orthogonal
    Punk; Kohstall
  7. Tan relations and universal short-range properties [advanced]
    usually one discusses universal long-range properties, but dilute gases also have new universal short-range properties connected by the Tan relations
    Zwerger, ch. 6 (by Braaten)
  8. Kosterlitz-Thouless transition in two-dimensional systems [advanced]
    in two dimensions, quantum fluctuations can be so strong that they destroy long-range order, but superfluidity is still possible
    Pitaevskii 6.7, 17.5; (Cardy 6.2, 6.4?)
  9. Nonequilibrium dynamics and integrability [advanced]
    how does a closed quantum system equilibrate and thermalize? in most system even an eigenstate will look thermal, but in one dimension there can be so many conservation laws that it keeps a memory of its initial state
    Kinoshita; Rigol; Polkovnikov, ch. III
  10. Localization in many-body systems [advanced]
    in disordered system with a random potential some or all wavefunction may become localized; recent questions involve localization in interacting systems and the breakdown of equilibrium statistical mechanics
    tba

Literature

Prerequisites

  • Quantum Mechanics
  • Statistical Physics (recommended)
  • Condensed Matter Theory (useful)

Formalities

  • oral presentation max. 60 minutes, followed by discusssion
  • hand in writeup until three weeks after your seminar: an essay on your seminar topic, with full sentences, sketches/figures if you like, but not just your slides; max. 15 pages but you are very welcome to make it shorter
  • 6 credit points, grade composed of writeup, oral presentation, and participation in discussion
  • attendance is mandatory; please send me an email if you cannot come
  • it is recommended that we go over your talk together before your presentation; please make an appointment for, say, the Monday before your talk.