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)
   

Literature

• Bloch, Dalibard, and Nascimbene, Nature Phys. 8, 267 (2012)
• Bloch, Dalibard, and Zwerger, Rev. Mod. Phys. 80, 885 (2008)
• Cardy, Scaling and Renormalization in Statistical Physics, Cambridge Univ. Press (1996)
• Chevy, Phys. Rev. A 74, 063628 (2006)
• Dalibard, Varenna lecture notes (1998)
• Diehl, Innsbruck lecture notes (2013)
• Enss, Condensed Matter Theory lecture notes (2016) (for participants only)
• Feynman, Int. J. Theor. Phys. 21, 467 (1982)
• Jaksch et al., Phys. Rev. Lett. 81, 3108 (1998)
• Ketterle and Zwierlein, Varenna lecture notes (2008)
• Kinoshita, Wenger, and Weiss, Nature 440, 900 (2006)
• Kohstall et al., Nature 485, 615 (2012)
• Nandkishore and Huse, Many-body localization (2014)
• Pethick and Smith, Bose-Einstein Condensation in Dilute Gases, Cambridge Univ Press 2008
• Pitaevskii and Stringari, Bose-Einstein Condensation, Clarendon Press 2003
• Polkovnikov et al., Rev. Mod. Phys. 83, 863 (2011)
• Punk, Dumitrescu, and Zwerger, Phys. Rev. A 80, 053605 (2009)
• Rigol, Dunjko, and Olshanii, Nature 452, 854 (2008)
• Sa de Melo, Physics Today 61, 45 (2008)
• Zwerger (ed.), The BCS-BEC Crossover and the Unitary Fermi Gas, Springer Lecture Notes in Physics 836 (PDF available from the university library)

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; 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.

Teaching in previous semesters