Quantum matter at ultralow temperatures : proceedings of the International School of Physics "Enrico Fermi" course 191, Varenna on Lake Como, Villa Monastero, 7-15 July 2014 = Materia quantistica ultrafredda : rendiconti della Scuola Internazionale di Fis

The Enrico Fermi summer school on Quantum Matter at Ultralow Temperatures held on 7-15 July 2014 at Varenna, Italy, featured important frontiers in the field of ultracold atoms. For the last 25 years, this field has undergone dramatic developments, which were chronicled by several Varenna summer schools, in 1991 on Laser Manipulation of Atoms, in 1998 on Bose-Einstein Condensation in Atomic Gases, and in 2006 on Ultra-cold Fermi Gases. The theme of the 2014 school demonstrates that the field has now branched out into many different directions, where the tools and precision of atomic physics are used to realise new quantum systems, or in other words, to quantum-engineer interesting Hamiltonians. The topics of the school identify major new directions: Quantum gases with long range interactions, either due to strong magnetic dipole forces, due to Rydberg excitations, or, for polar molecules, due to electric dipole interactions; quantum gases in lower dimensions; quantum gases with disorder; atoms in optical lattices, now with single-site optical resolution; systems with non-trivial topological properties, e.g. with spin-orbit coupling or in artificial gauge fields; quantum impurity problems (Bose and Fermi polarons); quantum magnetism. Fermi gases with strong interactions, spinor Bose-Einstein condensates and coupled multi-component Bose gases or Bose-Fermi mixtures continue to be active areas. The current status of several of these areas is systematically summarized in this volume. Title Page -- Contents -- Preface -- Course group shot -- Introduction to the physics of artificial gauge fields -- Magnetism and quantum physics -- Gauge invariance -- Cyclotron motion and Landau levels -- The Aharonov-Bohm effect -- Rotating gases -- Geometric phases and gauge fields for free atoms -- Berry's phase -- Adiabatic following of a dressed state -- The two-level case -- Validity of the adiabatic approximation -- Spontaneous emission and recoil heating -- Non-Abelian potentials and spin-orbit coupling -- Non-Abelian potentials in quantum optics