Quantum Optics

2.

Quantization of the Electromagnetic Field

2.1.

Field Quantization in Cavities

2.1.1.

2.1.1.1.

Boundary Conditions

2.1.1.2.

Standing Wave Solutions

2.1.1.3.

2.1.1.4.

Frequency Spectrum

2.1.2.

Classical Field Energy

2.1.2.1.

2.1.2.2.

Total Energy Expression

2.1.3.

Canonical Quantization

2.1.3.1.

Field Variables as Operators

2.1.3.2.

Canonical Commutation Relations

2.1.3.3.

Creation and Annihilation Operators

2.1.4.

Quantized Field Hamiltonian

2.1.4.1.

Mode Decomposition

2.1.4.2.

Number Operator

2.1.4.3.

Zero-Point Energy

2.2.

Free Field Quantization

2.2.1.

Plane Wave Expansion

2.2.1.1.

Fourier Decomposition

2.2.1.2.

Polarization Vectors

2.2.1.3.

2.2.2.

Quantization Volume

2.2.2.1.

Periodic Boundary Conditions

2.2.2.2.

2.2.3.

Field Operators

2.2.3.1.

Position and Momentum Representations

2.2.3.2.

2.2.3.3.

Heisenberg Picture

2.2.4.

2.2.4.1.

Ground State Definition

2.2.4.2.

Vacuum Fluctuations

2.2.4.3.

Zero-Point Motion

2.3.

Photon Properties

2.3.1.

Photon as Field Quantum

2.3.1.1.

Energy and Momentum Relations

2.3.1.2.

Massless Particle Properties

2.3.2.

Photon Number States

2.3.2.1.

2.3.2.2.

Number Operator Eigenvalues

2.3.3.

Photon Angular Momentum

2.3.3.1.

Spin Angular Momentum

2.3.3.2.

Orbital Angular Momentum

2.3.3.3.

2.3.4.

Photon Statistics

2.3.4.1.

Poissonian Distribution

2.3.4.2.

Sub-Poissonian Statistics

2.3.4.3.

Super-Poissonian Statistics

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3. Quantum States of Light