Strongly Correlated Systems in Atomic and Condensed Matter Physics

Abstract

This course will review recent progress in realizing strongly correlated many-body systems with ultracold atoms. Both theory and experiments will be discussed with an emphasis on the connection between the physics of ultracold atoms and correlated electron systems. The course will explore unique features of ultracold atoms such as dynamical control of Hamiltonians and single atom resolution.

Objective

This course provides the background needed to understand current research in ultracold atoms. Lecture material is complemented by homework problems that give hands-on experience with the concepts introduced in class, as well as a final project that involves reviewing an influential paper in a relevant research area and presenting a summary in class.

Content

Subjects covered in this class include: Bose-Einstein condensation of weakly interacting atomic gases; analogue gravity with BEC; spinor condensates; noninteracting atoms in optical lattices and probes of band structure; state dependent lattices and synthetic gauge fields; Bose Hubbard mode; quantum magnetism with ultracold atoms in optical lattices; quantum noise measurements as a probe of many-body states; Feshbach resonance; fermion pairing close to Feshbach resonance; the BCS-BEC crossover; polarons in systems of bosonic and fermionic ultracold atoms; fermionic Hubbard model; realizing and probing topological states with ultracold atoms; one dimensional systems; SU(N) magnetism and Kondo physics with alkaline-earth atoms; systems with long range interactions; many body localization; superradiance and Dicke quantum phase transitions in optical cavities for bosonic and fermionic atoms.

Resources