Optics: Fundamentals of geometrical optics. Waves. Sinusoidal waves. Plain waves. Refraction index. Polarization, diffraction. Propagation in anisotropic and inhomogeneous media (photonic crystals). Gaussian beams, Bessel beams, Laguerre-Gauss beams. Outline of “singular” optics. Outline of spectroscopy.

Nonlinear Optics: Polarization vector. Intuitive explanation of optics nonlinearities. Nonlinear susceptibility tensor, second order effects. Production of second harmonic and parametric processes, third order effects. Nonlinear refraction index self-focusing e self-defocusing. Parametric processes.

Laser (quantum electronics): Structure of matter. Plasmon. Principles of radiation-matter interaction. Continuous and pulsed laser systems. Parametric oscillators. Q-dots. Photonic crystal laser. Nanolaser. Integrated fibers. Nonlinear integrated fibers. In-out coupling of the radiation in embedded systems.

Optoelectronicdevices: Semiconductors and III-IV compounds. Homojunctions, heterojunctions and quantum wells. Junction photodetectors: pn, pin, avalanche photodetectors, single photon avalanche diodes. Noise in photodetectors, connection signal-noise, sensibility, BER and Q in optic receivers. Photodetector quantum limit. Fiber optics: typologies, electromagnetic propagation, dispersion (modal, chromatic and polarized), losses and nonlinear effects. Optical amplification: saturation, bandwidth, noise figure. Light guides in organic and inorganic dielectrics. Couplers, junctions to X, Y, and integrated interferometers. Electro-optic and acoustic-optic modulators. Optical logic gates.

Information Theory: Review of probability theory, random variables, stochastic processes, stationarity and ergodicity, examples: Gaussian processes and Markov chains – Shannon, Renyi and Von Neumann entropies, relative entropy, Kullback Leibler distance, mutual information, sufficient statistics, Fano’s inequality, Shannon theorem on source coding, Kraft inequality, Huffman codes – Channel capacity, Shannon theorem on channel coding, examples: capacity of binary symmetric channel; capacity of Gaussian channel – Fundamentals of rate-distortion theory, maximum entropy principle

Quantum Information I: Classical Electrodynamics: fundamental equations and dynamical variables. Quantum Electrodynamics in the Coulomb Gauge: general framework, time evolution, observables and states of the quantized free field, the Hamiltonian for the Interaction between particles and field. Coherent interaction: two state dynamics, Jaynes-Cummings model. Quantum Statistics of the field. Dissipative processes. Dressed states.

Quantum Information II: Finite-Dimensional Hilbert Spaces: Quantum bits, Multiple qubits, Quantum Tomography, Entanglement, Bell Inequality, Teleportation, No-cloning. Quantum Information Theory: Entropy and Information, the Holevo Bound, Communication over noise quantum channels, entanglement as physical resource. Quantum dense coding and quantum cryptography. Infinite-Dimensional Hilbert Spaces.

Quantum Computing: Quantum circuits. Single and multiple qubits gates Quantum Fourier transform and its applications. Quantum search algorithms.

Devices for quantum computing: Conditions for quantum computation. Harmonic oscillator quantum computer. Optical quantum computer. Ion traps. Nuclear magnetic resonance. Other implementation schemes.

During the Optics courses a Laboratory course will be performed on the optical phenomena and devices described in the lectures given in the theoretical units, in particular: Classical Optics; Geometrical optics; Interference; Diffraction; Twyman-Green; Michelson and Mach-Zehnder interferometers; Grating diffraction; Monochromators; Optical fibres and Losses measurement in fibre optics communications.

Lasers: Pumping systems; Resonators; Gaussian beams; CW lasers; Q-Switched lasers; Modelocked lasers; Semiconductor lasers.

Quantum Optics: Experiments under low photon number conditions, Quantum beam-splitter, Anti-bunching.

Nonlinear Optics: Second harmonic generation, Pockels effect.