The course aims to provide the basic notions and the analytical methods for the quantum description of the radiation field, and its interaction with matter. The principal quantum states of radiation are discussed, and measurement and interferometry processes are described in detail. In particular, fundamental topics of quantum mechanics applied to interaction with single atoms and with circuits based on superconductors are examined in depth. The course also includes a discussion on the relevant technological applications of quantum optics in its more recent developments, such as atomic fountain clocks and the practical use of squeezed states.
Expected learning outcomes
At the end of the course the student is expected to acquire the following knowledge:
1) The student will be able to discuss the quantization of the radiation field starting from classical electrodynamics; 2) He will be able to characterize the main observables and the most relevant states of the field of radiation, classic and nonclassical; 3) He will know the basic elements of the quantum theory of coherence and of the radiation detection. 4) He will know how to describe the generation and manipulation of nonclassical states via parametric processes, with particular regard to the properties of squeezing and entanglement; 5) He will be able to discuss the dynamics of the radiation field as an open quantum system; 6) He will be able to discuss the models and the dynamics of the interaction of the quantized field with atoms on two levels; 7) He will know how to describe various optical-quantum systems in fundamental experiments and in applications to quantum information.
Lesson period: Second semester
(In case of multiple editions, please check the period, as it may vary)
1) Quantization of the classical electromagnetic field. Field operators and density matrix. Fock space and photons. Thermal radiation. The vacuum state of the quantum radiation field and its physical effects. 2) Coherent states and their properties. Poisson distribution. Displacement operator and BCH formulas. Quadrature operators. 3) Quantum theory of radiation detection. Photoelectric effect. Theory of spatial and temporal coherence, related fundamental experiments. 4) Emission and absorption of radiation. Microscopic interaction and quantum dynamics of a two-level atom: Jaynes-Cummings model and dressed states. 5) Moment generating functions and probability distributions. Generalized Wigner functions. Gaussian states and their description. 6) Non-classical states of radiation. States with minimal indeterminacy and squeezed states. Squeezing operator. 7) Description of open systems in quantum optics. Dissipation and Master Equation models. Fokker-Planck equation. Decoherence. 8) Quantum mechanics of the beam splitter. Effective Hamiltonian and evolution of the fields. Mixing of two photons and fluorescence from a single atom. Quantum efficiency modeling with a beam splitter. Duality squeezing/entanglement. 9) Quantum measurements. Detection of the photon number. Homodyne and heterodyne detection. Quantum tomography. 10) Technological applications. The atomic clock and the atomic fountain clock. Squeezing and interferometry. Quantum teleportation.
Prerequisites for admission
Fundamental concepts of: a) non relativistic quantum mechanics, in particular for the description of atomic energy levels; b) classical electromagnetic field and electromagnetic waves in vacuum; c) basic optical instrumentation
The course is provided through lectures and classroom discussions. The attendance is strongly recommended.
The topics covered in the course can be found in the lecture notes and in key articles, downloadable from the University's ARIEL educational website http://fcastellioq.ariel.ctu.unimi.it/v3/Home/ Some recommended books for further information: 1) L. Mandel, E. Wolf '' Optical Coherence and Quantum Optics '', Cambridge University Press 2) G.Grynberg, A. Aspect and C. Fabre '' Introduction to Quantum Optics '', Cambridge University Press 3) R. Puri, '' Mathematical methods of quantum optics '', Springer (Berlin) 4) G.S.Agarwal '' Quantum Optics '', Cambridge University Press
Assessment methods and Criteria
The examination consists of an interview that focuses on the topics covered in the course. During the exam, lasting an average of 1 hour, both the skills and the critical abilities acquired by the student in the quantum description of the radiation field and its interaction with atoms will be evaluated, also on the basis of knowledge of fundamental experiments.