This course aims to introduce the physics, technology and performance of photonic devices that are employed for generation, manipulation, and detection of the quantum states of light for applications in the cutting-edge field of quantum information (quantum communication, quantum cryptography, quantum computing). Photonics is a key enabling technology for ICT and nowadays many “classical” and commercial photonic devices are based on nanostructure semiconductor materials exploiting quantum effects (for example quantum well, quantum dot and quantum cascade lasers, inter band photodetectors). Moreover, in recent years quantum technologies in the field of photonics have moved a step further by demonstrating the possibility to generate, manipulate and detect quantum states of light. After review of the classical theory of electromagnetic waves propagation in vacuum and in structured dielectric materials (e.g. optical waveguides and fibers), described by the Maxwell Equations, in the first part of the course, its second part will present the working principles of the main photonic devices (semiconductor lasers, modulators, photodetectors, and front-end circuits) employed in a classical optical communication, in information processing and transmission and their current implementation in different technological platforms. This will provide a necessary background to understand the peculiar features of a new generation of quantum optoelectronic devices required for applications in quantum information. In the third part of the course examples of purely quantum or “non-classical” radiation states (e.g., squeezed states, entangled states, photon antibunching) that are the cornerstone of quantum communication, quantum cryptography and quantum computing protocols will be presented both in the framework of the electromagnetic field quantization theory and following a more phenomenological approach. Then in the fourth part, the attention will be moved on the description of the working principles and recent implementations of photonic devices and optical systems able to generate, manipulate and detect quantum states of light such as single photon sources and detectors. This part of the course will also concern commercially available optical components that find applications in e.g. quantum optical communication. Students will analyze the main technologies and their general performance with the aim of being able to read data sheets and compare different available solutions. A selection of devices at research level, but with high Technology Readiness Levels, will also be presented and compared with the current commercial solutions. Emphasis will be also posed on photonic integrated circuits as they might represent the suitable platform for on-chip quantum states manipulation for applications in quantum technologies. Exercises on numerical (through MATLAB routines) and analytical solutions of typical problems in quantum photonics will be presented to provide a student’s hands-on learning.

The students will learn the basics of photonic devices and systems aimed at the generation and detection and manipulation of coherent light. Moreover, trough an introduction to the electromagnetic field quantization theory, they will acquire the necessary knowledge to understand the peculiar properties of quantum states of light, that do not have a classical counterpart, the working principles and the technological issues related to the realization of a new generation devices aimed at their generation, manipulation, and detection as single-photon semiconductor sources and detectors. This will 1) enable students to understand the main technological, experimental, and theoretical state of the art achievements and challenges in the photonic domain of the quantum information systems that promise to revolutionise the modern world; 2) to gather the ability to solve new practical problems in the field of quantum photonics.

- Principles of quantum mechanics - Principles of solid state and semiconductor physics - Fundamentals of electronic devices - Principle of classical optics and electromagnetic wave propagation in 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.

I. PART I (10 hours) Classical optics and electromagnetics. 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 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 - Coherence and correlation functions in the classical domain - Basic principles of optical waveguides and optical modes - Principles non-linear optical phenomena and nonlinear optics in semiconductors (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 for Electromagnetic Waves (EMW) propagation: plane waves, polarization, power and intensity, reflection, diffraction, and interference - Principles of optical waveguides and calculation of the optical modes of simple optical waveguides. Optical waveguides in photonic integrated circuits (for examples in a silicon photonic platform) - Non-linear optical phenomena and nonlinear optics in semiconductors (e.g. parametric down conversion and four-wave mixing) II. PART II (20 hours) Classical optical information: fundamentals and technologies - Radiation-matter interaction - Spontaneous emission, stimulated emission and absorption - Light emitting diode and laser diodes (including quantum well, quantum dot and quantum cascade lasers). State of the art technologies - Coherent emission (laser phase and intensity noise) - Principles of optical modulators - Technologies for the modulation of the light for transmission of the information: (OOK; PAM-4; BPSK, QPSK modulations) - Photodetectors, noise in photodetectors and optical receivers - Homodyne and Heterodyne detection - Photonic integrated circuits and integrated passive optical components (waveguides, ring resonators, switches, MZI, polarization splitters etc…). Silicon photonics III. PART III (15 hours) Fundamentals of quantum photonics - Review of the quantum harmonic oscillator - Number state operator - Quantization of electromagnetic field - Coherent states - Squeezed quantum states - Phenomenological approach to photon statistics: Poissonian, Super-Poissonian and Sub-Poissonian - Sub-Poissonian quantum states: states without non-classical counterpart Sub-Poissonian light generation by LEDs and laser diodes - Second order correlation function: Photon bunching and antibunching - Photon’s entanglement - Encoding quantum information in a single photon: polarization encoding, path encoding, orbital angular momentum encoding, time-bin and time-frequency encoding IV. PART IV (15 hours) Optical technologies for quantum information: applications in quantum optical communications and quantum computing - 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 - Photonic integrated circuits for manipulation of single – or multi-photons (Silicon on insulator platforms or LiNbO3 platforms) - Optical technologies for detection of quantum states of light: photon number resolving detectors (PNR) and non-PNR detectors; single photon counting modules - Examples of applications to quantum optical communications and quantum computing

Apart from the theoretical lectures there will be classroom exercises and laboratories of numerical calculus in MATLAB on the main courses’ topics (around 10 hours).

Lectures and Exercises Main references book: Quantum Optics. An introduction, M. Fox (OUP Oxford) Nonlinear optical systems, L. Lugiato, F. Prati, M. Brambilla (Cambridge University Press) Diode lasers and photonic integrated circuits, L. A. Coldren (Wiley), S. W. Corzine, L.M. Masanovic For further readings [1] Classical electrodynamics, J.D. Jackson (John Wiley & Sons) [2] Fundamentals of Photonics, B. E. A. Saleh, M. C. Teich (Wiley) [3] Semiconductor devices for high speed optoelectronics, G. Ghione (Cambridge University) [4] Nonlinear optics, R. Boyd (Elsevier) [5] The quantum theory of light, R. Loudon (Oxford Science Pubblications) [6] Quantum Optics, M. O. Scully, M. S. Zubairy (Cambridge University) [7] Semiconductor Laser Physics, W. W. Chow , S. W. Koch , M. Sargent (Springer) [8] Lasers, A. E. Seigman (University Science Books) [9] Quantum electronics, A. Yariv (Wiley) [10] A collection of recent review papers on the most advanced topics in the field of quantum photonics 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 during the course.

Modalità di esame: Prova scritta (in aula); Prova orale facoltativa;

Exam: Written test; Optional oral exam;

... The exam is divided in: 1) a mandatory written test composed by closed and open answers under teacher supervision (or on the available e-learning platform); 2) an optional oral exam. 1) The mandatory test lasts two hours and consists of 13 multiple-choice questions, on theoretical topics and 2 open questions where the students are asked to solve exercises. All the 15 questions are aimed to evaluate the student’s degree of knowledge of the courses’ topics and their ability to use the theoretical tools provided by the course to solve practical problems of quantum photonics. 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. For each closed question there are four answers: one right, three wrong. The right answer is worth +1.6 points, each wrong answer is worth -1/3 points; a not given answer is worth 0. For each open question the given answer is worth up to +3 points, each answer not given is worth 0 points. The result of the written test PTEST, is considered positive with PTEST (rounded to the nearest integer) ≥ 15. A bonus of +3 points is the added to PTEST to obtain the final mark for the part 1) of the exam as M1=((PTEST rounded to the nearest integer)+3 )/30. 2) To increase the final mark 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 most relevant course topics. The mark for the oral article presentation M2 ranges from 1/30 to 4/30. If the optional oral part is not chosen by the student M2=0. The final mark of the exam M is M1+M2 rounded to the nearest integer. Mark M1+M2 bigger than 30.5/30 are converted in a final mark M=30 e lode/30.

Gli studenti e le studentesse con disabilità o con Disturbi Specifici di Apprendimento (DSA), oltre alla segnalazione tramite procedura informatizzata, sono invitati a comunicare anche direttamente al/la docente titolare dell'insegnamento, con un preavviso non inferiore ad una settimana dall'avvio della sessione d'esame, gli strumenti compensativi concordati con l'Unità Special Needs, al fine di permettere al/la docente la declinazione più idonea in riferimento alla specifica tipologia di esame.