LFU:online

Institut für Theoretische Physik Institut für Theoretische Physik

assoz. Prof. Dr. Sebastian Diehl assoz. Prof. Dr. Sebastian Diehl

705904

Many-Body Physics with Ultracold Atoms

VO 2

4

wöch.

2-Jahresrhythmus

Englisch

The course encompasses an introduction to various aspects of the theory of ultracold quantum gases. We provide an overview of concepts needed to work in this field by focussing on concrete and prominent physical situations. We will discuss the many-body physics of both bosonic and fermionic systems in the continuum as well as on the optical lattice in thermodynamic equilibrium, also paying attention to the microscopic origin of the respective models. On the methodological side, the functional integral formulation of many-body systems will be introduced and applied to various situations.

Scales and interactions in ultracold gases; microscopic modelling, effective low energy Hamiltonian for alkali atoms. -- Weakly interacting bosons: Gross-Pitaevski equation and Bogoliubov theory; condensation vs. superfluidity. -- Transition to functional integral formulation; symmetry breaking, Goldstone theorem. -- Weakly interacting fermions: BCS theory; strongly interacting fermions: Feshbach resonances, BCS-BEC crossover. -- Optical lattices: microscopic derivation of Bose-Hubbard model, Mott-Insulator to superfluid quantum phase transition. Miscellaneous topics (if time allows): -- Advanced field theoretical techniques (Functional Renormalization Group) applied to strongly interacting ultracold quantum systems . -- Many-body physics with open quantum systems: dissipative quantum state preparation, dynamical phase transitions.

Requirements: Statistical mechanics including second quantization; basic knowledge of atomic physics and quantum field theory is helpful but not mandatory.
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