http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
Playing a prominent role in communications, quantum science and laser physics, quantum nonlinear optics is an increasingly important field. This book presents a self-contained treatment of field quantization and covers topics such as the canonical formalism for fields, phase-space representations and the encompassing problem of quantization of electrodynamics in linear and nonlinear media. Starting with a summary of classical nonlinear optics, it then explains in detail the calculation techniques for quantum nonlinear optical systems and their applications, quantum and classical noise sources in optical fibers and applications of nonlinear optics to quantum information science. Supplemented by end-of-chapter exercises and detailed examples of calculation techniques in different systems, this book is a valuable resource for graduate students and researchers in nonlinear optics, condensed matter physics, quantum information and atomic physics. A solid foundation in quantum mechanics and classical electrodynamics is assumed, but no prior knowledge of nonlinear optics is required.
1. Classical nonlinear optics -- 1.1. Linear polarizability -- 1.2. Nonlinear polarizability -- 1.3. Frequency dependence and dispersion -- 1.4. Power and energy -- 1.5. Order-of-magnitude estimates -- 1.6. The two-level atom -- 1.7. Local-field corrections -- 1.8. Propagation in a nonlinear medium -- 1.9. Raman processes -- Additional reading -- Problems -- 2. Field quantization -- 2.1. Quantum theory -- 2.2. Fock space for bosons -- 2.3. Many-body operators -- 2.4. Fock space for fermions -- 2.5. Canonical quantization -- 2.6. One-dimensional string -- 2.7. Scattering matrix -- 2.8. Quantized free electromagnetic field -- 2.9. Constrained quantization -- 2.10. Exponential complexity -- Additional reading -- Problems -- 3. Quantized fields in dielectric media -- 3.1. Dispersionless linear quantization -- 3.2. Scattering in linear media -- 3.3. Quantizing a nonlinear dielectric -- 3.4. Homogeneous nonlinear dielectric -- 3.5. Inhomogeneous nonlinear dielectric.
Contents note continued: 3.6. Dispersion -- 3.7. One-dimensional waveguide -- Additional reading -- Problems -- 4. Microscopic description of media -- 4.1. The Coulomb gauge -- 4.2. The multipolar gauge -- 4.3. Hamiltonian for a polarizable medium -- 4.4. Dipole-coupling approximation -- 4.5. Linear medium -- 4.6. Quantization of the linear model -- 4.7. Two-level atomic medium -- 4.8. Polaritonic limit -- Additional reading -- Problems -- 5. Coherence and quantum dynamics in simple systems -- 5.1. Photon counting and quantum coherence -- 5.2. Quadratures and beam-splitters -- 5.3. Coherent states and P-representations -- 5.4. Nonclassical states -- 5.5. Two-mode states -- 5.6. Mode entanglement -- 5.7. Parametric interactions -- 5.8. Anharmonic oscillator and Schrodinger's cat -- 5.9. Jaynes--Cummings dynamics -- 5.10. Parametric approximation -- Additional reading -- Problems -- 6. Decoherence and reservoirs -- 6.1. Reservoir Hamiltonians -- 6.2. Absorption -- 6.3. Gain -- 6.4. Phase decoherence.
Contents note continued: 6.5. Input--output relations -- 6.6. Photon flux and density -- 6.7. Two-time correlation functions -- 6.8. Master equations -- 6.9. Gain and damping rates -- 6.10. Driven linear cavity example -- Additional reading -- Problems -- 7. Phase-space distributions -- 7.1. Diffusion processes -- 7.2. Fokker--Planck equations -- 7.3. Stochastic differential equations -- 7.4. Phase-space representations -- 7.5. Wigner and Q-representations -- 7.6. Nonclassical representations -- 7.7. Operator identities and quantum dynamics -- 7.8. Quasi-probability Fokker--Planck equation -- 7.9. Linearized fluctuation theory -- 7.10. Functional phase-space representations -- Additional reading -- Problems -- 8. Single-mode devices -- 8.1. Linear cavity -- 8.2. Phase-space representation methods -- 8.3. Driven nonlinear absorber -- 8.4. Squeezing and photon anti-bunching -- 8.5. High-Q laser -- 8.6. Laser linewidth -- 8.7. Laser quantum state: number or coherent? -- 8.8. Open nonlinear interferometer.
Contents note continued: Additional reading -- Problems -- 9. Degenerate parametric oscillator -- 9.1. Hamiltonian and stochastic equations -- 9.2. Classical results -- 9.3. Fokker--Planck and stochastic equations -- 9.4. Adiabatic approximation -- 9.5. Multi-mode treatment of parametric down-conversion in a cavity -- Additional reading -- Problems -- 10. Quantum field dynamics -- 10.1. Kerr medium -- 10.2. Quantum solitons -- 10.3. Time-dependent Hartree approximation -- 10.4. Quantum solitons in phase space -- 10.5. Parametric down-conversion -- 10.6. Maxwell--Bloch equations -- Additional reading -- Problems -- 11. Quantum propagation in fibers and waveguides -- 11.1. Order-of-magnitude estimates -- 11.2. Waveguide modes -- 11.3. Dispersive energy -- 11.4. Nonlinear Hamiltonian -- 11.5. Fiber optic Hamiltonian -- 11.6. Raman Hamiltonian -- 11.7. Gain and absorption -- 11.8.Combined Heisenberg equations -- 11.9. Phase-space methods -- 11.10. Polarization squeezing -- Additional reading -- Problems.
Contents note continued: 12. Quantum information -- 12.1. The Einstein--Podolsky--Rosen paradox -- 12.2. Bell inequality -- 12.3. Schrodinger cat paradoxes -- 12.4. Probabilistic simulations of Bell violations -- 12.5. Quantum cloning -- 12.6. Teleportation -- Additional reading -- Problems.
Peter D. Drummond, Swinburne University of Technology, Melbourne, Mark Hillery, Hunter College, City University of New York.
Includes bibliographical references and index.