The quantum theory of nonlinear optics /

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 an...

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Bibliographic Details
Main Author:	Drummond, P. D. (Peter D.), 1950-
Other Authors:	Hillery, Mark Stephen
Format:	Book
Language:	English
Published:	Cambridge ; New York : Cambridge University Press, 2014.
Subjects:	Nonlinear optics. Quantum optics. Quantum theory.

Table of Contents:

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.