Hystorical introduction to the physics of ultra-cold atoms. Bosonic and Fermionic quantum degeneracy. Theory and experiments on quantum gases superfluidity. Gases in periodic potentials: how to simulate conduction of electrons in solids. Bose-Hubbard model. Superfluid-Mott insulator transition. Localization for a matter wave in a disordered potential. Simulation of magnetic phases. Dipolar gases. Creation of entangled states for quantum metrology in atomic clocks and interferometers.
Proceedings of the International School of Enrico Fermi CXL, "Bose Einstein Condensation in Atomic Gases ", Società Italiana di Fisica, 1999.
Proceedings of the International School of Enrico Fermi CXL, "Ultra-cold Fermi gases", Società Italiana di Fisica, 2007.
K. Huang, "Statistical Mechanics", John Wiley & Sons, 1987.
C. J. Pethick & H. Smith, "Bose-Einstein Condensation in Dilute Gases", Cambridge University Press, 2002. di Fisica, 2007.
Learning Objectives
Knowledge:
Properties of degenerate quantum gases and their use in the quantum simulation of quantum phenomena of condensed matter: conduction, superfluidity, magnetism, phase transitions. Knowledge of fundamental concepts of quantum metrology with ultra-cold atoms in atomic clocks and interferometers.
Skills acquired:
Application of theoretical knowhow to the comprehension of experiments on quantum gases. Capability to identify experimental methods for analysis and characterization of atomic ultra-cold samples. Ability in the simplification of the description of a quantum phenomenon.
The final examination consists in an oral exam where the student must summarize the content of scientific articles in the field of quantum gases. Knowhow about theoretical concepts and experimental methodologies will be verified.
Course program
Historical introduction to the physics of quantum gases: from liquid Helium di ultra-cold atomic gases.
Quantum degenerate bosonic and fermionic atoms in an harmonic potential. Bose Einstein Condensation. Excitation spectrum of a bosonic degenerate gas. Fermionic degeneracy and BCS theory of the fermionic superfluidity. Josephson junction with ultra-cold atoms.
Gases in reduced dimensionalities. 1Dimension: Tonks-Girardeau gas, fermionization of bosons due to repulsive interactions.
2Dimensions: BKT transition.
Gases in periodic potentials. Bose Hubbard model. Superfluid-Mott insulator phase transition. Fermionic Hubbard model: how to simulate the electronic conduction in solids using ultra-cold atomic gases. Anderson model and the phenomenon of localization of a matter wave in a disordered potential.
Magnetism. How to simulate magnetic phase in condensed matter using cold atoms. Intense magnetic fields using synthetic gauge fields. Topological phases. Dipolar gases with anisotropic and long range interactions.
Generation of entangled states for quantum metrology in atomic clocks and interferometers. N atoms in two modes with repulsive and attractive interactions: from Fock to Schroedinger cat states.