Ultracold Quantum Gases II – Topics

Outline of the course:

• Short introduction into quantum gases (BEC, Fermi gas)
• Interactions between atoms (s-wave scattering, Feshbach resonances, BEC-BCS crossover)
• Cold atoms in periodic potentials
• Double-well pheonomena
• Optical lattices (band structure)
• Spin-dependent lattices (two-electron atoms)
• Hubbard models (bosonic, fermionic)
• Quantum phases of the Hubbard model
• Detection techniques (time-of-flight, noise correlations)
• Quantum Gas Microscopy
• Working principle (spin- and charge-resolved imaging)
• Imaging bosonic and fermionic Mott insulating states
• Detecting correlations and hidden order parameters
• Spin models and quantum magnetism
• Superexchange interactions (double-well, extended lattice)
• Magnon bound states
• Frustrated models
• Geometric properties and topology of energy bands
• Berry phase in two-level system (spin 1/2 in magnetic field)
• Berry connection/Berry curvature in periodic systems
• Examples: SSH model and graphene
• Detection via interferometry
• Artificial gauge fields and Chern insulators
• Review basics of the integer quantum Hall effect (bulk-edge correspondence)
• Topological lattice models (Hofstadter, Haldane)
• Realization of topological bands with cold atoms
1. Lattice shaking
2. Laser-assisted tunneling / Raman coupling
3. Topological charge pumping
• Methods for measuring Chern numbers
• Topology in periodically-driven systems (anomalous Floquet)

• Thermalization in closed quantum systems
• Eigenstate thermalization hypothesis
• Introduction to Anderson localization and many-body localization
• Measurement and detection schemes
• Long-range interacting quantum gases
• Dipolar gases
• Rydberg atoms
• Magnetic atoms

Literature

Review paper on laser cooling:

• W. D. Phillips, Nobel lecture: Laser cooling and trapping of neutral atoms, Rev. Mod. Phys. 70, 721 (1998)

Review papers:

• F. Dalfovo, S. Giorgini, L. P. Pitaevskii, and S. Stringari, Theory of Bose-Einstein condensation in trapped gases, Rev. Mod. Phys. 71, 463 (1999)
• S. Giorgini, L. P. Pitaevskii, and S. Stringari, Theory of ultracold atomic Fermi gases, Rev. Mod. Phys. 80, 1215 (2008)
• I. Bloch, J. Dalibard, and W. Zwerger, Many-body physics with ultracold gases, Rev. Mod. Phys. 80, 885 (2008)
• R. Nandkishore and D. A. Huse, Many-body localization and thermalization in quantum statistical mechanics, Ann. Rev. of Cond. Matt. Phys. 6, 15-38 (2015)
• F. Alet, N. Laflorencie, Many-body localization: An introduction and selected topics, Comptes Rendus Physique 19, 498-525 (2018)
• N. R. Cooper, J. Dalibard, and I. B. Spielman, Topological bands für ultracold atoms, Rev. Mod. Phys. 91, 015005 (2019)

Books

• C. J. Pethick and H. Smith, Bose-Einstein Condensation in Dilute Gases, Cambridge University Press (2002)
• L. P. Pitaevskii and S. Stringari, Bose-Einstein Condesation, Oxford University Press (2003)
• M. Lewenstein, A. Sanpera, V. Ahufinger, Ultracold Atoms in Optical Lattices: Simulating quantum many-body systems, OUP Oxford

The university library is currently getting many new e-books. Please check their website to find the books mentioned above!