href="#ulink_608de50a-b9a6-5de4-897b-e38db1bc60e0">1. Brief description of the dressed-atom method 2. Weak coupling domain 3. Strong coupling domain 4. Modifications of the field. Dispersion and absorption Complement DXX Light shifts: a tool for manipulating atoms and fields 1. Dipole forces and laser trapping 2. Mirrors for atoms 3. Optical lattices 4. Sub-Doppler cooling. Sisyphus effect 5. Non-destructive detection of a photon Complement EXX Detection of one- or two-photon wave packets, interference 1. One-photon wave packet, photodetection probability 2. One- or two-photon interference signals 3. Absorption amplitude of a photon by an atom 4. Scattering of a wave packet 5. Example of wave packets with two entangled photons
9 Chapter: XXI QUANTUM ENTANGLEMENT, MEASUREMENTS, BELL’S INEQUALITIES A. Introducing entanglement, goals of this chapter B. Entangled states of two spin-1/2 systems C. Entanglement between more general systems D. Ideal measurement and entangled states E. “Which path” experiment: can one determine the path followed by the photon in Young’s double slit experiment? F. Entanglement, non-locality, Bell’s theorem COMPLEMENTS OF CHAPTER XXI, READER’S GUIDE Complement AXXI Density operator and correlations; separability 1. Von Neumann statistical entropy 2. Differences between classical and quantum correlations 3. Separability Complement BXXI GHZ states, entanglement swapping 1. Sign contradiction in a GHZ state 2. Entanglement swapping Complement CXXI Measurement induced relative phase between two condensates 1. Probabilities of single, double, etc. position measurements 2. Measurement induced enhancement of entanglement 3. Detection of a large number Q of particles Complement DXXI Emergence of a relative phase with spin condensates; macroscopic non-locality and the EPR argument 1. Two condensates with spins 2. Probabilities of the different measurement results 3. Discussion
10 Appendix IV: Feynman path integral 1. Quantum propagator of a particle 2. Interpretation in terms of classical histories 3. Discussion; a new quantization rule 4. Operators
11 Appendix V: Lagrange multipliers 1. Function of two variables 2. Function of AT variables
12 Appendix VI: Brief review of Quantum Statistical Mechanics 1. Statistical ensembles 2. Intensive or extensive physical quantities
13 Appendix VII: Wigner transform 1. Delta function of an operator 2. Wigner distribution of the density operator (spinless particle) 3. Wigner transform of an operator 4. Generalizations 5. Discussion: Wigner distribution and quantum effects
15 Index
List of Illustrations
1 Chapter XVFigure 1: Physical interaction between two identical particles: initially in the…Figure 2: Two diagrams representing schematically the two terms appearing in equ…Figure 3: Schematic representation of a direct term (left diagram where each par…
2 Complement BXVFigure 1: Quantum distribution functions of Fermi-Dirac 