The students will learn the basics of photonic devices and systems aimed at the generation, detection and manipulation of coherent classical light. Moreover, trough an introduction to the electromagnetic field quantization theory and photon statistics, they will acquire the necessary knowledge to understand the peculiar properties of quantum states of light, i.e. that do not have a classical counterpart, the working principles and the technological issues related to the realization of new devices aimed at their generation, manipulation, and detection in the field quantum information that promise to revolutionize the modern world. At the end of the course the students are also expected to gather 1. the ability to solve standard practical problems in the field of quantum photonics, 2. the ability to critically read and understand the scientific literature in the field of quantum photonics, 3. the ability to interact with other experts in the field of quantum information encoding and processing.

- Principles of quantum mechanics - Principles of solid state and semiconductor physics - Principles of electronic and quantum devices - Principles of classical optics and electromagnetic wave propagation in vacuum and dielectric materials. NOTE: The students without this background will have the possibility to follow a split-class program of 10 hours to gain the main concepts of electromagnetism and optics necessary to attend this course.

The course is divided in IV parts or modules MODULE I (10 hours). Split class program Classical optics and Electromagnetism. Elements of nonlinear optics Class 1 (with no background in Electromagnetism and Optics) - Classical theory of Maxwell Equations (ME) for Electromagnetic Waves (EMW) propagation - Solutions of ME in vacuum and homogeneous, linear, isotropic and non-dispersive media (harmonic plane waves and spherical waves) - Polarization of the electromagnetic field (linear polarization, elliptical polarization) - Pointing vector (and EMW mean intensity) - Reflection, diffraction, and Interference of EMW (different types of interferometers: Michelson, Mach-Zehnder (MZI)) - Coherence and correlation functions in the classical domain - Basic principles of optical waveguides and optical modes - Principles of nonlinear optical phenomena (e.g. parametric down conversion and four-wave mixing) Class 2 (with some background in Electromagnetism and Optics) - Review of the theory of Maxwell Equations (ME) for Electromagnetic Waves (EMW) propagation. Plane waves and spherical waves, polarization, power and intensity, reflection, diffraction, and interference (different types of interferometers: Michelson, Mach Zender (MZI)) - Coherence and correlation functions in the classical domain - Optical waveguides and calculation of the optical modes of simple optical waveguides. Optical waveguides in photonic integrated circuits - Nonlinear optical phenomena and nonlinear optics in semiconductors (e.g. parametric down conversion and four-wave mixing) MODULE II (20 hours) Classical optical information processing. Principles and technologies - Radiation-matter interaction (two level approximation) - Spontaneous emission, stimulated emission and absorption of light - Light emitting diode and laser diodes (including Quantum Well, Quantum Dots and Quantum Cascade Lasers). State of the art technologies. Coherent emission (laser phase and intensity noise) - Optical modulators. Technologies and protocols for light modulation for transmission of the optical information - Photodetectors and optical receivers. Homodyne and Heterodyne detection - Hints on photonic integrated circuits and integrated passive optical components (waveguides, ring resonators, switches, MZI, polarization splitters etc…). Silicon photonics MODULE III (15 hours) Fundamentals of quantum photonics - Introduction to quantum optics - Phenomenological approach to photon optics. Poissonian, Super-Poissonian and Sub-Poissonian statistics. - States without non-classical counterpart. Sub-Poissonian light generation by LEDs and laser diodes - Second order correlation function. Photon bunching and antibunching - Quantization of electromagnetic field. Review of the quantum harmonic oscillator. Number state operator. Coherent states and squeezed quantum states - Single photon and entangled photons states - Hints on encoding quantum information in a single photon. Polarization encoding, path encoding, orbital angular momentum encoding, time-bin and time-frequency encoding MODULE IV (15 hours) Optical technologies for quantum information - Examples of optical technologies and experimental set-up for generating quantum states of light as single photons, entangled photons, squeezed states. Heralded single photon source, FWM in waveguides and micro- resonators, semiconductor quantum dots in micro-cavities, degenerate down conversion processes - Hints on photonic integrated circuits for manipulation of single – or multi-photons states (Silicon on Insulator platforms or LiNbO3 platforms) - Examples of optical technologies for detection of quantum states of light. Photon number resolving detectors (PNR) and non-PNR detectors. Single photon counting modules - [Optional: some applications to quantum optical communications and quantum computing]

The course is divided in theoretical lectures and classroom exercises on the lectures arguments aimed to provide to the students practical procedures for solving typical problems in the field of quantum photonics. Some laboratories (‘hands-on’ sessions) of numerical calculus in MATLAB on specific course topics will be proposed to the students without any required report.

Lectures and Exercises Main references books: [a] Quantum Optics. An introduction, M. Fox (OUP Oxford) [b] Fundamentals of Photonics, B. E. A. Saleh, M. C. Teich (Wiley) [c] Nonlinear optical systems, L. Lugiato, F. Prati, M. Brambilla (Cambridge University) [d] Diode lasers and photonic integrated circuits, L. A. Coldren S. W. Corzine, L.M. Masanovic (Wiley) [e] Introduction to Fiber-Optic Communications, R. Hui (Elsevier) For further reading: [1] Classical electrodynamics, J.D. Jackson (John Wiley & Sons) [2] Nonlinear optics, R. Boyd (Elsevier) [3] Quantum electronics, A. Yariv (Wiley) [4] Semiconductor devices for high speed optoelectronics, G. Ghione (Cambridge University) [5] Semiconductor Laser Physics, W. W. Chow , S. W. Koch , M. Sargent (Springer) [6] Lasers, A. E. Seigman (University Science Books) [7] The quantum theory of light, R. Loudon (Oxford Science Pubblications) [8] Quantum Optics, M. O. Scully, M. S. Zubairy (Cambridge University) Numerical Calculus: Numerical calculus using Matlab, J. H. Mathews, K. D. Fink (Prentice Hall) NOTE: Other useful material and meta-material will be uploaded on the course material webpage before or during the course.

Lecture slides; Exercises; Exercise with solutions ; Lab exercises; Lab exercises with solutions; Multimedia materials;

Exam: Written test; Optional oral exam;

The exam aims to verify the acquisition of the students' skills detailed in the “Expected learning outcomes” section. In particular, the exam is divided in: 1) a compulsory written text; 2) an optional oral exam. The compulsory written text is aimed at evaluating the students’ acquisition of a) the basic knowledge of photonic devices and systems aimed at the generation, detection and manipulation of coherent classical light and quantum states of light mainly for applications in the field of optical information encoding and processing; b) their ability to use the theoretical tools provided by the course to solve practical problems in quantum photonics. The oral part is aimed at evaluating the students’ awareness of critically read and understand the recent scientific literature in the field of quantum photonics. 1) The compulsory test lasts two hours and consists of 12 multiple-choice questions on theoretical topics with only one right answer and a penalty for each incorrect answer, and 3 open questions where the students are asked to solve exercises or answer to theoretical questions. During the written test it is not possible to consult any type of material (e.g. textbooks, personal notes, lecture slides). The use of personal calculators is permitted only if it is a not programmable. The final mark M1 for the part 1) of the exam can reach a maximum value of 27/30. 2) To increase the final mark of the exam up to 30 e lode/30 the students may choose to present a research article chosen by the teacher and/or his/her collaborators on the course topics. The mark for the oral article presentation M2 ranges from 1/30 to 3/30. If the optional oral part is not chosen by the students then: M2=0. The final mark of the exam is M=M1+M2 rounded to the nearest integer. The upgrade from 30/30 to 30 e lode/30 is decided by the teacher based on his/her considerations regarding the comprehensive student performance and level of preparation.

In addition to the message sent by the online system, students with disabilities or Specific Learning Disorders (SLD) are invited to directly inform the professor in charge of the course about the special arrangements for the exam that have been agreed with the Special Needs Unit. The professor has to be informed at least one week before the beginning of the examination session in order to provide students with the most suitable arrangements for each specific type of exam.