Stark korrelierte Quantensysteme in Atomphysik und kondensierter Materie
Strongly Correlated Quantum Systems in Atomic and Condensed Matter Physics

This course will focus on recent progress in realizing strongly-correlated many-body systems with ultracold atoms. Both theoretical ideas and recent experimental results will be reviewed. Throughout the class the relations between many-body systems of ultracold atoms and condensed matter will be emphasized. We will also discuss unique features of ultracold atomic systems, such as control of band structures and interaction, availability of new probes, and the possibility to study nonequilibrium quantum dynamics and disordered quantum systems.

A tentative outline of lectures:
1) Introduction to many-body physics with cold atoms
2) Bose-Einstein condensation of weakly interacting atoms
3) Noninteracting atoms in optical lattices: Engineering band structures and topological states
4) Interacting lattice bosons: phase diagram and nonequilibrium dynamics
5) Low energy collisions and Feshbach resonances
6) Ultracold Fermi gases: BEC-BCS crossover
7) Realizing quantum impurity systems with cold atoms: orthogonality catastrophe and beyond
8) Quantum magnetism with ultracold atoms
9) Interferometric probes of many-body systems
10) Disordered and interacting many-body systems: Many-body localization

The practical classes support the lectures with tutorials and problem sets. The tutorials cover basic theoretical concepts of many-body physics such as an (i) introduction to second quantization, (ii) Green's functions and linear response theory, and (iii) Fermi's Golden rule, etc. The problem sets will help to understand and deepen the physical concepts presented in the lecture.

Das Erreichen der Lernergebnisse wird zu gleichen Teilen an Hand 1. der schriftlich einzureichenden Lösungen zu den Übungsaufgaben sowie 2. einer abschließenden Projektarbeit mit Präsentation der Ergebnisse bewertet.