Quantum Optics, as the child of Optics and Quantum Mechanics, has inherited a double linearity: that of Maxwell equations, which use optical modes as a basis of solutions, and that of the Schrödinger equation, which uses quantum state bases. Considering these two bases on an equal footing and tailoring quantum fields not only in given modes, but also optimizing the spatiotemporalshapes of the modes in which the state is defined, has not been so far fully exploited. This specific feature of Quantum Optics opens wide perspectives for treating complex quantum states. These lectures give an introduction to this subject, at the frontier between classical optics and quantum optics. One shows how to experimentally determine the full multimode covariance matrix characterizing the complex system at the quantum level. and stresses the importance of the possibility of changing modal bases, and to extract physical modes from experimental data. Applications to information processing and high sensitivity optical measurements are also considered.
Quantum optics, optical modes, quantum correlations and entanglement, optical coherence