Quantum Optics
A.Y. 2022/2023
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.
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.
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: First semester
Assessment methods: Esame
Assessment result: voto verbalizzato in trentesimi
Single course
This course cannot be attended as a single course. Please check our list of single courses to find the ones available for enrolment.
Course syllabus and organization
Single session
Responsible
Lesson period
First semester
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. Coherence theory.
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. Squeezing and interferometry. Quantum teleportation.
2) Coherent states and their properties. Poisson distribution. Displacement operator and BCH formulas. Quadrature operators.
3) Quantum theory of radiation detection. Photoelectric effect. Coherence theory.
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. 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 following textbooks 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
Moreover, the topics covered can be partly found in lecture notes and in key articles, downloadable from the University's ARIEL educational website.
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
Moreover, the topics covered can be partly found in lecture notes and in key articles, downloadable from the University's ARIEL educational website.
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.
Professor(s)
Reception:
By appointment only (upon agreement by email)
Professor's office: Physics Department, LITA building, room A5/C13