Coursebooks 2017-2018

PDF
 

Cold atoms and quantum simulation

PHYS-410

Lecturer(s) :

Brantut Jean-Philippe

Language:

English

Summary

This course describes the concept of quantum simulation and its implementation using cold atomic gases. The experimental tools and core theoretical concepts are presented, together with a few topics of ongoing research in the field.

Content

Basic tools of the physics of cold atoms:

  1. Introduction: basics of atomic physics, alkali atoms. Reminders on the two level system, forces on two-level atoms. Cooling and trapping of neutral atoms.
  2. Ideal Bose and Fermi gases: reminders of quantum statistical mechanics, trapped gases. Experimental aspects.
  3. Effective Hamitonians: adiabatic elimination of fast degrees of freedom, moving frames
  4. Optical lattices: band theory and tight binding models, fundamental exemples
  5. Interactions between atoms: s-wave scattering, Feshbach resonances

Fundamental exemples of quantum simulations with cold atoms, chosen among:

  1. Interacting atoms in a lattice: Bose-Hubbard model, Superfluid to Mott insulator phase transition, Fermi Hubbard models.
  2. Quantum transport and disordered systems: Anderson localization, the Bose glass, many-body localization
  3. The unitary Fermi gas: Leggett theory of the BEC-BCS crossover, universality and Tan's relations
  4. Topological systems: artificial gauge fields and spin orbit coupling schemes, Haldane and Harper-Hofstatter models

Learning Prerequisites

Required courses

Quantum electrodynamics and quantum optics

Recommended courses

Solid state physics III

Important concepts to start the course

Basic quantum mechanics: hydrogen atoms, harmonic oscillators, two level systems, perturbation theory

Basic statistical mechanics: quantum statistics, density matrices

Quantum optics: two level system in an external field, Optical Bloch equations, stimulated and spontaneous emission

Learning Outcomes

By the end of the course, the student must be able to:

Transversal skills

Teaching methods

Lectures and exercise classes, paper clubs: each student will be given one research article to read and analyze, and then expose in class.

Assessment methods

Oral exam

Resources

Bibliography

Statistical mechanics, Kerson Huang

Laser cooling and trapping, Metclaf and Van der Straten

Bose-Einstein condensation in dilute gases,  Pethick and Smith

Quantum Fluids, Anthony Leggett

Atomes et Rayonnements, lectures by Jean Dalibard at Collège de France

Ressources en bibliothèque

In the programs

Reference week

 MoTuWeThFr
8-9     
9-10     
10-11     
11-12     
12-13     
13-14 GRA330   
14-15    
15-16 GRA330   
16-17    
17-18     
18-19     
19-20     
20-21     
21-22     
 
      Lecture
      Exercise, TP
      Project, other

legend

  • Autumn semester
  • Winter sessions
  • Spring semester
  • Summer sessions
  • Lecture in French
  • Lecture in English
  • Lecture in German