# 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

**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*

**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*

**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*

**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)*

**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*

**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*

**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)*

**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?)*

**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*

**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

- 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 (2015) (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)
- 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)
- Schaefer and Teaney, Rep. Prog. Phys. 72, 126001 (2009)
- 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; 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.