University of Heidelberg

Tilman Enss | Teaching — Theory of ultracold atoms

as of 10 Mar 2017

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]

Seminar Topics

  1. 2016-11-04: Scattering of ultracold atoms and Feshbach resonances [Enss]
    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
    seminar notes (for participants only)
  2. 2016-11-11: Bose-Einstein condensates and Bogoliubov theory [Aliaga Sirvent]
    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
    seminar notes (for participants only)
  3. 2016-11-25: Bose-Hubbard model and the Mott superfluid transition [Blumberg]
    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)
    seminar notes (for participants only)
  4. 2016-12-02: The BCS-BEC crossover [Wolff]
    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; Sa de Melo
    seminar notes (for participants only)
  5. 2016-12-09: Fermi polarons [Schiffer]
    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
    seminar notes (for participants only)
  6. 2016-12-16: Kosterlitz-Thouless transition in two-dimensional systems [Karle]
    in two dimensions, phase 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?)
    seminar notes (for participants only)
  7. 2017-01-13: Nonequilibrium dynamics and integrability [Ihrig]
    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
    seminar notes (for participants only)
  8. 2017-01-20: Vortices in rotating Bose-Einstein condensates [Bernards]
    the dynamics of a BEC can be described by the Gross-Pitaevskii equation, which admits vortex solutions in a rotating BEC
    Pitaevskii, ch. 5
    seminar notes (for participants only)



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


  • 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; pay attention to bibliography; 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.