Table of Contents

""Cover""; ""Contents""; ""List of participants""; ""1 Strongly correlated bosons and fermions in optical lattices""; ""1.1 Introduction""; ""1.2 Optical lattices""; ""1.3 The Bose�Hubbard model and the superfluid to Mott insulator transition""; ""1.4 One-dimensional bosons and bosonization""; ""1.5 From free fermions to Fermi liquids""; ""1.6 Mott transition of fermions: three dimensions""; ""1.7 One-dimensional fermions""; ""1.8 Conclusion""; ""Acknowledgements""; ""References""; ""2 Ultracold atoms in optical lattices""; ""2.1 Overview""; ""2.2 Introduction"" ""2.3 Basics of optical lattices""""2.4 Detection methods""; ""2.5 Bose� and Fermi�Hubbard models""; ""2.6 Quantum magnetism with ultracold atoms in optical lattices""; ""2.7 Single-site and single-atom resolved imaging of quantum gases in optical lattices""; ""References""; ""3 The few-atom problem""; ""3.1 Overview""; ""3.2 The two-body problem and resonance width""; ""3.3 Basics of the three-body problem with short-range interactions""; ""3.4 The method of Skorniakov and Ter-Martirosian (STM) for few-body problems with resonant short-range interactions""; ""3.5 Final remarks"" ""6.1 The dipole�dipole interaction""""6.2 Dipolar Bose�Einstein condensates""; ""6.3 Dipolar gases in optical lattices""; ""6.4 Conclusions""; ""References""; ""7 Ultracold polar molecules""; ""7.1 Motivation and challenges""; ""7.2 Making ultracold polar molecules""; ""7.3 Characterizing the ultracold polar molecules""; ""7.4 Ultracold chemistry, dipolar interactions, and reduced dimensionality""; ""Acknowledgements""; ""References""; ""8 Ultracold Fermi gases as quantum simulators of condensed matter physics""; ""8.1 Introduction""; ""8.2 The non-interacting Fermi gas"" ""8.3 Fermionic super.uidity and the BEC�BCS crossover""""8.4 Probing the fermionic superfluid""; ""8.5 Conclusion""; ""References""; ""9 Competing instabilities in quench experiments with ultracold Fermi gases near a Feshbach resonance""; ""9.1 Overview""; ""9.2 Introduction""; ""9.3 Linear response and collective modes""; ""9.4 Feshbach resonance via pseudo-potentials""; ""9.5 Application to pairing susceptibility""; ""9.6 More on Stoner instability""; ""9.7 Discussion""; ""9.8 Concluding remarks""; ""Acknowledgements""; ""References"" ""Acknowledgements""""References""; ""4 Entanglement in many-body quantum systems""; ""4.1 Introduction""; ""4.2 Entanglement in many-body systems: pure states""; ""4.3 Entanglement in many-body systems: mixed states""; ""4.4 Entanglement and area laws""; ""4.5 Tensor network states""; ""4.6 Conclusions""; ""References""; ""5 Quantum Hall states of ultracold atomic gases""; ""5.1 Introduction""; ""5.2 Rapid rotation""; ""5.3 Optically induced gauge fields""; ""5.4 Bose gases""; ""5.5 Fermi gases""; ""5.6 Summary""; ""Acknowledgements""; ""References""; ""6 Theory of dipolar gases"" This title provides authoritative tutorials on the most recent achievements in the field of quantum gases at the interface between atomic physics and quantum optics, condensed matter physics, nuclear and high-energy physics, non-linear physics and quantum information.