Quantum optics

A.Y. 2020/2021
Overall hours
Learning objectives
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.
Course syllabus and organization

Single session

Lesson period
Second semester
The lectures can be delivered entirely remotely, according to the official calendar, in case of mobility restrictions due to the health emergency. In this case, the Zoom platform will be used with connection to a virtual classroom of the Physics Department, in synchronous connection and with real-time interaction between students and the teacher. In the lesson we will use a graphic tablet and the projection of slides. At the request of students it is possible to organize tutoring meetings in presence. The (oral) exams will always be carried out with the Zoom platform, in a virtual classroom or in a dedicated virtual meeting. Program and reference materials are not changed.
Course syllabus
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
Teaching methods
The teaching is provided through lectures and classroom discussions. Attendance is strongly recommended.
Teaching Resources
The topics covered can be found largery in lecture notes and in key articles, downloadable from the University's ARIEL educational website http://fcastellioq.ariel.ctu.unimi.it/v3/Home/
Moreover, for completeness and further information some books are recommended:
1) C.G.Gerry and P.L.Knight, "Introductory Quantum Optics", Cambridge University Press 2005
2) G.Grynberg, A.Aspect and C.Fabre ''Introduction to Quantum Optics'', Cambridge University Press
3) G.S.Agarwal ''Quantum Optics'', Cambridge University Press
4) L. Mandel, E. Wolf ''Optical Coherence and 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. The evaluation of the exam result is in thirtieths.
FIS/03 - PHYSICS OF MATTER - University credits: 6
Lessons: 42 hours
tuesday 14:30 - 19:00
Department of Physics, via Celoria 16 Milan (fifth floor, room A/5/C3)
by e-mail appointment
Room A/5/C8 - 5th floor LITA building, Dipartimento di Fisica (via Celoria, 16 - 20133 Milano)