Quantum Optics

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. The main new topics included in the revised edition are 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.
The fundamentals of quantum optics are introduced in a sufficient depth for their practical application and for an understanding and treatment of specialized problems of modern research.
The rigorous development of quantum optics in the context of quantum field theory and the attention spent to details make this a valuable book for graduate students as well as for researchers.
Important topics are presented in a unified manner on the basis of a quantum–field–theoretical approach:quantization of the electromagnetic field in linear mediaminimal coupling, multipolar coupling, dipole approximation,
rotating–wave approximation, effective Hamiltonianssource–attributed light and time–dependent field commutation
rulesnumber states, coherent states, squeezed states, quadrature
states, phase statesphase–space representationsdamped quantum systemsinput–output relationsphotoelectric counting, correlation techniques,
spectral measurements and homodyne detectionquantum–state measurement and reconstructionnonclassical lightmeasurement–based nonclassicality and entanglement
criteriaspontaneous emission and resonance fluorescencevan der Waals and Casimir forcesJaynes––Cummings model and cavity QEDquantized motion of a trapped atom

Spis treści:
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–l