QUANTUM OPTICS

The course is one of the educational activities of the Master Degree in Engineering Physics and enables the student to gain knowledge and understanding of fundamental and applied concepts in the field of quantum optics, which is the description of the quantum features of light.
The objective of the course is to provide a strong background in the field of quantum optics, which is at the foundation of the current applications and implementations in the fields of optical quantum information processing, quantum communication, quantum computing, quantum sensing and quantum technologies.

At the end of the course, the student will:
• Know the basic principles of quantum mechanics
• Know quantum optics methodologies and modern applications (quantum technologies)
• Know how to generate, measure and exploit non-classical light
• Be able to describe the optical (linear and non-linear) systems typically used in modern quantum optics laboratories
• Be able to solve simple quantum mechanical/optical problems and exercises
• Be able to understand scientific literature papers in the field of quantum optics

Knowledge of Calculus, Linear Algebra and Physics I-II is required. Basic knowledge of Quantum Mechanics may be helpful, but it is not necessary since it will be reviewed in the course.

1. Introduction to Quantum Optics
Historical introduction
Wave-particle duality
Lagrangian and Hamiltonian formulations of a physical theory

2. The Formalism of Quantum Mechanics
Entities and rules in a physical theory
States and observables
Measurement of observables, expectation values, and time evolution
Schrödinger, Heisenberg, and interaction pictures
Quantum harmonic oscillator
Heisenberg uncertainty principle
Composite systems and entanglement
Bell test of local realism

3. Quantization of the Electromagnetic Field
Canonical quantization
Classical Hamiltonian of the electromagnetic field
Quantum Hamiltonian of the electromagnetic field
Single-mode states and operators

4. Quantum States of Light
Fock states
Thermal states
Coherent states
Squeezed states

6. Tools of Quantum Optics
Beam splitter
Interferometry
Theory of optical coherence: classical and quantum coherence functions
Encoding quantum information using polarization
PBS (polarizing beam splitters) and wave plates to control polarization
Continuous-mode quantum optics
Time bin encoding of quantum information

7. Measurement of the Quantum State of Light
Photodetection
Homodyne detection
Heterodyne detection

8. Generating Quantum States of Light
Elements of perturbation theory (interaction picture)
Elements of nonlinear optics
Spontaneous Parametric Down-Conversion
How to generate entangled photons and squeezed light

9. Probability Distributions in Phase Space in Quantum Optics
Distributions in classical and quantum phase space
Wigner function: introduction, properties, and examples
Other distributions: Weyl correspondence, parametrized distributions, P-function, Q-function

• Gerry, Christopher; Knight, Peter, Introductory Quantum Optics. Cambridge: Cambridge University Press, 20041028.
• Leonhardt, Ulf, Measuring the quantum state of light. Cambridge: Cambridge University Press, 1997.

The achievement of the course objectives is assessed through a final oral exam.

The exam consists of two parts conducted in a single interview, in English.
1. A 20-25 minute seminar on a topic chosen by the student from those covered in class or from additional topics suggested by the instructor or the student themselves. The student should present the general concepts of the topic in a correct and comprehensive manner, providing examples at the level of the lectures and the textbook. Students are encouraged to seek original examples, applications, and connections with other topics to demonstrate a high level of understanding. The seminar may be delivered using slides or directly on the board.
2. Two to three questions on the core material of the course as presented in the lectures. The student must answer (if necessary, with the support of the board) to demonstrate their understanding of the fundamental concepts and notions of the course. Both theoretical and experimental aspects will be considered equally important.

A fully successful exam (27-30/30) will be achieved when a solid and extensive command of the concepts discussed in class is demonstrated. An average grade (22-26/30) will reflect a fairly comprehensive understanding of individual topics but with limited connections between them. A passing level (18-21/30) will correspond to a minimal knowledge of individual notions.

The teaching takes place through frontal lessons on the blackboard or with slides, with the possibility of interaction and involvement.
There will be 3 laboratory activities to experimentally investigate the concepts and techniques described in the course.

English

All course topics are presented in the classroom and covered by the lecture notes provided by the teacher.
Lecture notes can be integrated with textbooks.
The list of the topics covered lesson by lesson will be made available, as well as the material (notes, slides, papers, etc) provided by the teacher.