The quantum description of light
- Classical eletromagnetic theory: Maxwell equation, potentials, wave equation
- quantization in a cavity, modal expansion
- The harmonic oscillator in quantum mechanics
- Classical energy, quantization of the electric and magnetic fields, Fock states

2.Classical and quasi-classical states of the e.m. field
- The density operator formalism in quantum mechanics, pure and mixed states
- The thermal state, definition and properties
- The coherent states of the e.m. defined as eigenstates of the anihilation operator, and as state of minimum indeterminacy: number states and quadrature statistics.

3. single photon interferometry
- The beam splitter and the Mach-Zender interferometer in quantum optics.
- The single photon state. Experiment of Grangier et al. (1986).
- Single photon interferometry, wave particle dualism. Wheeler and delay choice ecperiment (2007)
- The Hong Ou Mandel Effect

4. Non classical states of the e.m. field. squeezing and entanglement.
- The squeezed states of the e.m. field.
- Quasi-classical representation: the Wigner function.
- Squeezed vacuum state
- The coherent squeezed state
- Continuous variable entanglement: the two-mode squeezed state. Quadrature entanglement and EPR paradox.

5. Generation of entangled states from nonlinear crystal: twin beam and twin photons.
- Some nonlinear optics results
- Quantum description of parametric down-conversion (PDC)
- Entangled stated generation from PDC, twin beams.
- COmparison between classical and quantum correlations.
- Applications in metrology and quantum communications: high-senesitivity measurements exploiting quantum correlations.

6. Interaction betweeen quantized light and atomic systems.
- Interaction of a two-level atom woth single radiation mode.
Quantum electrodynamics in a cavity (Cavity QUED):
- The Rabi semi-classsical model
- The Jaymes Cumming quantum-mechanical mode
- Some hystorical cavity QED experiments.

7 Dissipation and decoherence. The Master equation in Quantum Optics.
- The Master Equation in the Born and Markov approximations.
- 2-level atom interacting with a continuum of modes of the e.m. modes in free space.
- kramers Kroenig relations between the dispersive and dissipative contributions. Detailled balanced. Calculation of the dissipative coefficients for the 2-level atom.
- Equilibrium approach (rate equation, decoherence,equations for the mean values)