Degree course: 
Corso di Second cycle degree in Physics
Academic year when starting the degree: 
Academic year in which the course will be held: 
Course type: 
Compulsory subjects, characteristic of the class
Second semester
Standard lectures hours: 
Detail of lecture’s hours: 
Lesson (48 hours)

Knowledge of electromagnetism and basic quantum mechanics.

Voto Finale

Quantum Optics investigates the quantum-mechanical nature of light and its interaction with matter. Born at the beginning of the last century,this discipline has had over the last 30 years tremendous developments.
The course is a theoretical introduction to the matter The goal is to provide students with the essential formal tools to gain an insight into this fascinating subject, and illustrate the fundamental concepts in the light of some modern experiments.

1.The quantum description of light
-Refresh of classical electromagnetism: Maxwell equations, potentials, wave equation
-Quantization cavity, expansion in normal modes
-The harmonic oscillator in quantum mechanics
-The classical energy and its quantization.Quantized electric and magnetic fields.
-Fock states.

2.The classical and quasi-classical states of the electromagnetic field
-Recalls of quantum mechanical formalism, pure and mixed states
-The thermal equilibrium state, definition and properties.
-The coherent states of the e.m field (as eigenstates of the destruction operator, as a minimum uncertainty states, as displaced vacuum): statistics of the photon number and of the field quadratures.

3.Interferometry with single photons
- The beam-splitter and the 'Mach Zehnder interferometer in quantum optics.
- The single photon state, the experiment of Grangier et al. (1986).
- Single photon Interferometr, wave-particle duality. Weeheler conceptual experiment of delayed choice(2007) and interaction free measurements.
- The Hong-Ou-Mandel effect:
- Partition of N photons on a beam-splitter

4. The non-classical states of the electromagnetic field: squeezed and entangled states
- Squeezed states of the electromagnetic field
- Quasi-classical representations: the Wigner function
- The squeezed vacuum state
- Squeezed coherent states
- Continuous-variable entanglement: the two-mode squeezed state, quadrature entanglement and EPR paradox

5. Generation of entangled states in non-linear crystals:twin photons and twin beams.
- Elements of Nonlinear Optics.
- Quantum description of parametric frequency down-conversion (PDC)
- State formalism for the PDC process: entangled state, twin beams
- Comparison between correlations of quantum and classical origin
- Examples of quantum metrology applications: high sensitivity interferometry with squeezed light, high sensitivity detection with quantum correlation.

6. Interaction of light with quantized atomic systems
- Interaction of a two-level atom with a single mode of the radiation field. The regime of cavity quantum electrodynamics (Cavity QED)
- The semi-classical model
- The quantum-mechanical Jaymes-Cummings model
- Introduction to historical experiments in cavity quantum electrodynamics (the Haroche group at ENS Paris)

7. Dissipation and decoherence: the Master Equation in quantum optics
- The Master Equation in the Born and Markov approximations
- The two-level atom interacting with the continuum of modes of the e.m. field in free space.
- Kramers-Kronig relations for the dispersive and dissipative contributions. Evaluations of the dissipative coefficients for the two-level atom.
- Approach to equilibrium (rate equations, .decoherence, evolution of mean values)