Physics

RINALDO TROTTA
RINALDO TROTTA

The student will acquire knowledge of the fundamental principles of light-matter interaction studied via semi-classical and quantum approaches. Moreover, the student will study different aspects related to the quantum mechanical nature of light and its characterization according to photon statistics. During the course, the student will also deal with non-linear optics and will study some practical applications of quantum optics.
A - Knowledge and understanding
OF 1) To understand the fundamentals of quantum optics and non linear optics.
OF 3) To understand phenomena related to light-matter interaction, using both semi-classical and quantum approaches.
B - Application skills
OF 4) To be able to use semi-classical and quantum approaches to understand phenomena related to the interaction of light with matter.
OF 5) To be able to apply the basic principles of quantum optics to solve simple problems related to the knowledge acquired during the course.
C - Autonomy of judgment
OF 6) To be able to evaluate which optical phenomena require a classical or quantum treatment of the electromagnetic field to be explained.
OF 7) To develop quantitative reasoning abilities and problem-solving skills, which represent the basis to study, model and understand quantum phenomena related to light-matter interaction.
D - Communication skills
OF 8) To know how to communicate the knowledge acquired during the course via presentation of a scientific work related to one particular topic discussed during the lecture.
E - Ability to learn
OF 9) Have the ability to consult scientific papers in the field of quantum optics.
OF 10) Have the ability to understand practical applications that use the basic principles of quantum optics.

The student will acquire the fundamentals of quantum optics and will understand phenomena related to light-matter interaction, using both semi-classical and quantum approaches.

a) Knowledge of the fundamentals of electromagnetism is essential
b) Knowledge of the fundamentals of quantum mechanics is essential.
c) Knowledge of the fundamentals of optical laboratory is important.

Classical theory of coherence and statistical properties of radiation. Coherent and chaotic light. Semi-classical theory of photon detection. Characterization of light by photon statistics. Mach-Zehnder interferometer. Degree of first order coherence. Hanbury-Brown and Twiss interferometer. Degree of second order coherence. Experimental evidences of photon-antibunching. (15 hours)
Quantum theory of the electromagnetic field. Quantization of single mode and multimode fields. Fock states. Coherent states. Squeezed states. Quantum mechanics of the beam splitter. Quantum theory of the Hanbury-Brown and Twiss experiment. Single photon interference. Hong-Ou-Mandel interference. Time-resolved two-photon interference. (15 hours)
Atom-field interaction. Fermi’s golden rule. Interaction Hamiltonian. Perturbation theory for a 2-level system. Rabi oscillations. Spontaneous emission. Line broadening. Einstein coefficients. Optical Bloch equations. Damping of the Rabi Oscillations. Semi-classical theory of laser. Laser behaviour in steady-state and transient regime. Mode locking and ultrashort pulse laser. Fundamentals of non-linear optics. Electromagnetic field in a non-linear medium, semi-classical approach. (15 hours)
Full quantum treatment of light-matter interaction. Absorption and emission rates. The Jaynes-Cumming model. Quantized Rabi oscillations. Collapse and revival of Rabi oscillations. Cavity quantum electrodynamics: strong and weak coupling regimes. Weisskopf-Wigner theory of spontaneous emission. Weak coupling regimes: The Purcell effect. Source of single photons and photon pairs. Quantum treatment of parametric fluorescence. (15 hours)

1) Loudon, The quantum theory of ligh, Oxford University Press; 2) Gerry and Knight, Introductory quantum optics, Cambridge University Press ; 3) Fox, Quantum optics, an introduction, Oxford University Press; 4) Grynberf, Aspect, Fabre, Introduction to quantum optics, Cambridge University Press.

The course, of 6 credits, is carried out over 30 lessons of 2 hours each. These include theoretical lectures, with discussion of specific example selected from the literature. The topics covered in each part of the program are reported on the course website, with the indication of the suggested texts.

Lesson attendance is optional but highly recommended.

The final exam is an oral examination. Typically, the examination includes questions and written exercises on the contents of the course.
To pass the exam the student must be able to present a specific subject matter or a calculation described during the course, to apply the methods learned to examples and situations similar to those already discussed during the course.
In the evaluation, the following are taken into account:
- correctness and completeness of the concepts discussed;
- clarity and rigor in the discussion;
- analytical ability to handle theoretical concepts;
- problem solving ability (methods and results).

1. Describe the semi-classical theory of photo-detection.
2. Discuss the concept of optical coherence.
3. Describe how to quantize the electromagnetic field.
4. Describe the quantum theory of spontaneous emission.

• Photon Statistics


• Quantization of the electromagnetic field


• Light-matter interaction