This book provides an elementary introduction to the subject of quantum optics, the study of the quantum mechanical nature of light and its interaction with matter. The presentation is almost entirely concerned with the quantized electromagnetic field. Topics covered include single-mode field quantization in a cavity, quantization of multimode fields, quantum phase, coherent states, quasi-probability distribution in phase space, atom-field interactions, the Jaynes-Cummings model, quantum coherence theory, beam splitters and interferometers, dissipative interactions, nonclassical field states with squeezing etc., 'Schroedinger cat' states, tests of local realism with entangled photons from down-conversion, experimental realizations of cavity quantum electrodynamics, trapped ions, decoherence, and some applications to quantum information processing, particularly quantum cryptography. The book contains many homework problems and an extensive bibliography. This text is designed for upper-level undergraduates taking courses in quantum optics who have already taken a course in quantum mechanics, and for first and second year graduate students.
1. Introduction; 2. Field quantization; 3. Coherent states; 4. Emission and absorption of radiation by atoms; 5. Quantum coherence functions; 6. Beam splitters and interferometers; 7. Nonclassical light; 8. Dissipative interactions and decoherence; 9. Optical test of quantum mechanics; 10. Experiments in cavity QED and with trapped ions; 11. Applications of entanglement: Heisenberg-limited interferometry and quantum information processing; Appendix A. The density operator, entangled states, the Schmidt decomposition, and the von Neumann entropy; Appendix B. Quantum measurement theory in a (very small) nutshell; Appendix C. Derivation of the effective Hamiltonian for dispersive (far off-resonant) interactions; Appendix D. Nonlinear optics and spontaneous parametric down-conversion.