Cavity Quantum Electrodynamics -- Contents -- Preface -- Acknowledgments -- 1 Introduction -- 1.1 What is light? -- 1.1.1 Geometrical optics -- 1.1.2 Wave optics -- 1.1.3 Classical electrodynamics and relativity -- 1.1.4 Quantum mechanics and quantum electrodynamics -- 1.2 A brief history of cavity QED -- 1.3 A map of the book -- 1.4 How to read this book -- 2 Fiat Lux! -- 2.1 How to quantize a theory -- 2.2 Why the radiation field is special -- 2.3 What is a cavity? -- 2.3.1 What is resonance? -- 2.3.2 Confinement is the key -- 2.4 Canonical quantization of the radiation field -- 2.4.1 Quantization in a cavity -- 2.4.2 Quantization in free space -- 2.5 The Casimir force -- 2.5.1 Zero-point potential energy -- 2.5.2 Maxwell stress tensor -- 2.5.3 The vacuum catastrophe -- Recommended reading -- Problems -- 3 The photon's wavefunction -- 3.1 Position in relativistic quantum mechanics -- 3.2 Extreme quantum theory of light with a twist -- 3.3 The configuration space problem -- 3.4 Back to vector notation -- 3.5 The limit of vanishing rest mass -- 3.6 Second quantization -- Recommended reading -- Problems -- 4 A box of photons -- 4.1 The classical limit -- 4.1.1 Coherent states -- 4.1.2 The density matrix -- 4.1.3 The diagonal coherent-state representation -- 4.2 Squeezed states -- 4.2.1 The squeezing operator -- 4.2.2 Generating squeezed states -- 4.2.3 Geometrical picture -- 4.2.4 Homodyne detection -- Recommended reading -- Problems -- 5 Let matter be! -- 5.1 A single point dipole -- 5.2 An arbitrary charge distribution -- 5.3 Matter-radiation coupling and gauge invariance -- Recommended reading -- 6 Spontaneous emission -- 6.1 Emission in free space -- 6.2 Emission in a cavity -- Recommended reading -- 7 Macroscopic QED -- 7.1 The dielectric JCM -- 7.2 Polariton-photon dressed excitations -- 7.3 Quantum noise of matter and macroscopic averages.

7.4 How a macroscopic description is possible -- 7.5 The Kramers-Kronig dispersion relation -- 7.6 Including absorption in the dielectric JCM -- 7.7 Dielectric permittivity -- 7.8 Huttner-Barnett theory -- 7.8.1 The matter Hamiltonian -- 7.8.2 Diagonalization of the total Hamiltonian -- Recommended reading -- Problems -- 8 The maser -- the laser -- and their cavity QED cousins -- 8.1 The ASER idea -- 8.2 How to add noise -- 8.2.1 Einstein's approach to Brownian motion -- 8.2.2 Langevin's approach to Brownian motion -- 8.2.3 The modern form of Langevin's equation -- 8.2.4 Ito's and Stratonovich's stochastic calculus -- 8.3 Rate equations with noise -- 8.4 Ideal laser light -- 8.5 The single-atom maser -- 8.6 The thresholdless laser -- 8.7 The one-and-the-same atom laser -- Recommended reading -- Problems -- 9 Open cavities -- 9.1 The Gardiner-Collett Hamiltonian -- 9.2 The radiation condition -- 9.3 Natural modes -- 9.4 Completeness in general -- 9.4.1 Whittaker's scalar potentials -- 9.4.2 General formulation of the problem -- Recommended reading -- Problems -- Appendix A Perfect cavity modes -- Appendix B Perfect cavity boundary conditions -- Appendix C Quaternions and special relativity -- C.1 What are quaternions? -- C.2 Quaternion calculus -- C.3 Biquaternions and Lorentz transformations -- Appendix D The Baker-Hausdorff formula -- Appendix E Vectors and vector identities -- E.1 Relation between vector products and determinants -- E.2 Vector products and the Levy-Civita tensor -- E.3 The product of two Levy-Civita tensors as a determinant -- E.4 The vector product of three vectors -- E.5 Vectorial expressions involving del -- E.6 Some useful integral theorems -- Appendix F The Good, the Bad, and the Ugly -- F.1 Connections -- F.1.1 The rectangular barrierFI.1 The rectangular barrier -- F.1.2 The sine function.

F.1.3 The Lorentzian representation and the principal part -- F.1.4 The Gaussian -- F.1.5 The Laplacian of 1/r -- F.1.6 The comb function -- F.1.7 A general rule to find representations -- F.2 Product of two principal parts -- F.3 Discontinuous functions -- References -- Index.