Quantum Optics 3E

This is the third, revised and extended edition of the acknowledged "Lectures on Quantum Optics" by W. Vogel and D.-G. Welsch.
It offers theoretical concepts of quantum optics, with special emphasis on current research trends. A unified concept of measurement-based nonclassicality and entanglement criteria and a unified approach to medium-assisted electromagnetic vacuum effects including Van der Waals and Casimir Forces are the main new topics that are included in the revised edition. The rigorous development of quantum optics in the context of quantum field theory and the attention to details makes the book valuable to graduate students as well as to researchers.

Werner Vogel studied physics at the Friedrich-Schiller University of Jena, where he received his PhD in 1980 and worked as a research assistent at the Physics Department. After three postdoc years at the University of St. Petersburg, he finished his habilitation thesis in Jena and became Lecturer for Theoretical Physics at the College of Education in Güstrow in 1989. Since 1992, he has been Professor of Theoretical Physics at the University of Rostock.
Dirk-Gunnar Welsch studied physics at the Friedrich-Schiller University of Jena. After receiving his PhD in 1972, he worked as a postdoctoral research fellow at the Joint Institute for Nuclear Research in Dubna. From 1974 to 1994 he was a scientific assistent and later senior scientific assistent at the Physics Department of the University of Jena, where he finished his habilitation thesis in 1980. He has been Professor of Theoretical Physics at the University of Jena since 1994.

"... covers the basic concepts of quantum optics, as well as the more advanced aspects that are currently the subject of research around the world ... I recommend it to those ... who seek a well-rounded understanding of theoretical quantum optics." (Optics & Photonics News)

Preface.
1 Introduction.
1.1 From Einstein’s hypothesis to photon anti-bunching.
1.2 Nonclassical phenomena.
1.3 Source-attributed light.
1.4 Medium-assisted electromagnetic fields.
1.5 Measurement of light statistics.
1.6 Determination and preparation of quantum states.
1.7 Quantized motion of cold atoms.
2 Elements of quantum electrodynamics.
2.1 Basic classical equations.
2.2 The free electromagnetic field.
2.2.1 Canonical quantization.
2.2.2 Monochromatic-mode expansion.
2.2.3 Nonmonochromatic modes.
2.3 Interaction with charged particles.
2.3.1 Minimal coupling.
2.3.2 Multipolar coupling.
2.4 Dielectric background media.
2.4.1 Nondispersing and nonabsorbing media.
2.4.2 Dispersing and absorbing media.
2.5 Approximate interaction Hamiltonians.
2.5.1 The electric-dipole approximation.
2.5.2 The rotating-wave approximation.
2.5.3 Effective Hamiltonians.
2.6 Source-quantity representation.
2.7 Time-dependent commutation relations.
2.8 Correlation functions of field operators.
3 Quantum states of bosonic systems.
3.1 Number states.
3.1.1 Statistics of the number states.
3.1.2 Multi-mode number states.
3.2 Coherent states.
3.2.1 Statistics of the coherent states.
3.2.2 Multi-mode coherent states.
3.2.3 Displaced number states.
3.3 Squeezed states.
3.3.1 Statistics of the squeezed states.
3.3.2 Multi-mode squeezed states.
3.4 Quadrature eigenstates.
3.5 Phase states.
3.5.1 The eigenvalue problem of &Vcaron;.
3.5.2 Cosine and sine phase states.
4 Bosonic systems in phase space.
4.1 The statistical density operator.
4.2 Phase-space functions.
4.2.1 Normal ordering: The P function.
4.2.2 Anti-normal and symmetric ordering: The Q and theW function.
4.2.3 Parameterized phase-space functions.
4.3 Operator expansion in phase space.
4.3.1 Orthogonalization relations.
4.3.2 The density operator in phase space.
4.3.3 Some elementary examples.
5 Quantum theory of damping.
5.1 Quantum Langevin equations and one-time averages.
5.1.1 Hamiltonian.
5.1.2 Heisenberg equations of motion.
5.1.3 Born and Markov approximations.
5.1.4 Quantum Langevin equations.
5.2 Master equations and related equations.
5.2.1 Master equations.
5.2.2 Fokker–Planck equations.
5.3 Damped harmonic oscillator.
5.3.1 Langevin equations.
5.3.2 Master equations.
5.3.3 Fokker–Planck equations.
5.3.4 Radiationless dephasing.
5.4 Damped two-level system.
5.4.1 Basic equations.
5.4.2 Optical Bloch equations.
5.5 Quantum regression theorem.
6 Photoelectric detection of light.
6.1 Photoelectric counting.
6.1.1 Quantum-mechanical transition probabilities.
6.1.2 Photoelectric counting probabilities.
6.1.3 Counting moments and correlations.
6.2 Photoelectric counts and photons.
6.2.1 Detection scheme.
6.2.2 Mode expansion.
6.2.3 Photon-number statistics.
6.3 Nonperturbative corrections.
6.4 Spectral detection.
6.4.1 Radiation-field modes.
6.4.2 Input-output relations.
6.4.3 Spectral correlation functions.
6.5 Homodyne detection.
6.5.1 Fields combining through a nonabsorbing beam splitter.
6.5.2 Fields combining through an absorbing beam splitter.
6.5.3 Unbalanced four-port homodyning.
6.5.4 Balanced four-port homodyning.
6.5.5 Balanced eight-port homodyning.
6.5.6 Homodyne correlation measurement.
6.5.7 Normally ordered moments.
7 Quantum-state reconstruction.
7.1 Optical homodyne tomography.
7.1.1 Quantum state and phase-rotated quadratures.
7.1.2 Wigner function.
7.2 Density matrix in phase-rotated quadrature basis.
7.3 Density matrix in the number basis.
7.3.1 Sampling from quadrature components.
7.3.2 Reconstruction from displaced number states.
7.4 Local reconstruction of phase-space functions.
7.5 Normally ordered moments.
7.6 Canonical phase statistics.
8 Nonclassicality and entanglement of bosonic systems.
8.1 Quantum states with classical counterparts.
8.2 Nonclassical light.
8.2.1 Photon anti-bunching.
8.2.2 Sub-Poissonian light.
8.2.3 Squeezed light.
8.3 Nonclassical characteristic functions.
8.3.1 The Bochner theorem.
8.3.2 First-order nonclassicality.
8.3.3 Higher-order nonclassicality.
8.4 Nonclassical moments.
8.4.1 Reformulation of the Bochner condition.
8.4.2 Criteria based on moments.
8.5 Entanglement.
8.5.1 Separable and nonseparable quantum states.
8.5.2 Partial transposition and entanglement criteria.
9 Leaky optical cavities.
9.1 Radiation-field modes.
9.1.1 Solution of the Helmholtz equation.
9.1.2 Cavity-response function.
9.2 Source-quantity representation.
9.3 Internal field.
9.3.1 Coarse-grained averaging.
9.3.2 Nonmonochromatic modes and Langevin equations.
9.4 External field.
9.4.1 Source-quantity representation.
9.4.2 Input-output relations.
9.5 Commutation relations.
9.5.1 Internal field.
9.5.2 External field.
9.6 Field correlation functions.
9.7 Unwanted losses.
9.8 Quantum-state extraction.
10 Medium-assisted electromagnetic vacuum effects.
10.1 Spontaneous emission.
10.1.1 Weak atom–field coupling.
10.1.2 Strong atom–field coupling.
10.2 Vacuum forces.
10.2.1 Force on an atom.
10.2.2 The Casimir force.
11 Resonance fluorescence.
11.1 Basic equations.
11.2 Two-level systems.
11.2.1 Intensity.
11.2.2 Intensity correlation and photon anti-bunching.
11.2.3 Squeezing.
11.2.4 Spectral properties.
11.3 Multi-level effects.
11.3.1 Dark resonances.
11.3.2 Intermittent fluorescence.
11.3.3 Vibronic coupling.
12 A single atom in a high-Q cavity.
12.1 The Jaynes–Cummings model.
12.2 Electronic-state dynamics.
12.2.1 Reduced density matrix.
12.2.2 Collapse and revival.
12.2.3 Quantum nature of the revivals.
12.2.4 Coherent preparation.
12.3 Field dynamics.
12.3.1 Reduced density matrix.
12.3.2 Photon statistics.
12.4 The Micromaser.
12.5 Quantum-state preparation.
12.5.1 Schrödinger-cat states.
12.5.2 Einstein–Podolsky–Rosen pairs of atoms.
12.6 Measurements of the cavity field.
12.6.1 Quantum state endoscopy.
12.6.2 QND measurement of the photon number.
12.6.3 Determining arbitrary quantum states.
13 Laser-driven quantized motion of a trapped atom.
13.1 Quantized motion of an ion in a Paul trap.
13.2 Interaction of a moving atom with light.
13.2.1 Radio-frequency radiation.
13.2.2 Optical radiation.
13.3 Dynamics in the resolved sideband regime.
13.3.1 Nonlinear Jaynes–Cummings model.
13.3.2 Decoherence effects.
13.3.3 Nonlinear motional dynamics.
13.4 Preparing motional quantum states.
13.4.1 Sideband laser-cooling.
13.4.2 Coherent, number and squeezed states.
13.4.3 Schrödinger-cat states.
13.4.4 Motional dark states.
13.5 Measuring the quantum state.
13.5.1 Tomographic methods.
13.5.2 Local methods.
13.5.3 Determination of entangled states.
Appendix.
A The medium-assisted Green tensor.
A.1 Basic relations.
A.2 Asymptotic behavior.
B Equal-time commutation relations.
C Algebra of bosonic operators.
C.1 Exponential-operator disentangling.
C.2 Normal and anti-normal ordering.
D Sampling function for the density matrix in the number basis.
Index.