Informações sobre o curso
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This course gives you access to basic tools and concepts to understand research articles and books on modern quantum optics. You will learn about quantization of light, formalism to describe quantum states of light without any classical analogue, and observables allowing one to demonstrate typical quantum properties of these states. These tools will be applied to the emblematic case of a one-photon wave packet, which behaves both as a particle and a wave. Wave-particle duality is a great quantum mystery in the words of Richard Feynman. You will be able to fully appreciate real experiments demonstrating wave-particle duality for a single photon, and applications to quantum technologies based on single photon sources, which are now commercially available. The tools presented in this course will be widely used in our second quantum optics course, which will present more advanced topics such as entanglement, interaction of quantized light with matter, squeezed light, etc... So if you have a good knowledge in basic quantum mechanics and classical electromagnetism, but always wanted to know: • how to go from classical electromagnetism to quantized radiation, • how the concept of photon emerges, • how a unified formalism is able to describe apparently contradictory behaviors observed in quantum optics labs, • how creative physicists and engineers have invented totally new technologies based on quantum properties of light, then this course is for you....
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Sugerido: 7 weeks of study, 4-5 hours / week

Aprox. 28 horas restantes
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Legendas: English
Globe

cursos 100% online

Comece imediatamente e aprenda em seu próprio cronograma.
Calendar

Prazos flexíveis

Redefinir os prazos de acordo com sua programação.
Clock

Sugerido: 7 weeks of study, 4-5 hours / week

Aprox. 28 horas restantes
Comment Dots

English

Legendas: English

Programa - O que você aprenderá com este curso

1

Seção
Clock
5 horas para concluir

Quantization of light: one mode

In this first lesson, you will discover what is canonical quantization, apply it to the quantization of a single mode of the electromagnetic field, and find that it behaves as a quantum harmonic oscillator. The notion of photon will then naturally emerge, as well as the weird but fundamental notion of vacuum fluctuations....
Reading
13 vídeos (Total de 119 min), 3 leituras, 10 testes
Video13 videos
1.0 Introduction to Lesson 15min
1.1 Canonical quantization10min
1.2.1 Material harmonic oscillator /111min
1.2.2 Material harmonic oscillator /212min
1.3 Single mode of radiation9min
1.4 Canonical quantization of a single mode10min
1.5 Observables6min
1.6 Number states; Photon7min
1.7 Vacuum fluctuations5min
1.8 What have we learnt? What next?4min
Introduction to homework 111min
Quantization of classical oscillators12min
Reading3 leituras
Homework 1min
Correction of Homework 130min
Einstein's 1905 paper introducing the "photon"min
Quiz10 exercícios práticos
Questions about the general introduction8min
Practice quiz video 1.110min
Practice quiz video 1.2.14min
Video 1.2.2.6min
Video 1.34min
Video 1.48min
Video 1.52min
Video 1.72min
Video 1.82min
Homework 1 evaluation16min

2

Seção
Clock
3 horas para concluir

One photon state in a single mode: particle-like behaviour

In this lesson, you will discover how the quantum optics formalism leads to the particle-like behaviour of a one photon wave-packet. For this, you will have to learn the quantum optics expressions of the simple and joint photodetection signals. A comparison with the semi-classical expressions will illustrate the necessity of quantum optics....
Reading
7 vídeos (Total de 52 min), 2 leituras, 5 testes
Video7 videos
2.1 The semi-classical model of optics9min
2.2 One-photon state in a single mode10min
2.3 Photo-detection signals7min
2.4 Single photo-detection signal for a one photon state4min
2.5 Double photo-detection signal for a one photon state: a fully quantum behavior6min
2.6 Quantum optics: a must9min
Reading2 leituras
Homework 2min
Correction of Homework 230min
Quiz5 exercícios práticos
Video 2.14min
Video 2.22min
Video 2.32min
Video 2.68min
Homework 2 evaluation18min

3

Seção
Clock
3 horas para concluir

One photon interference: Wave-Particle duality

In this lesson, you will address the fascinating question of a single photon interfering with itself, by calculating the interference pattern for a single photon launched into a Mach-Zehnder interferometer. In order to do it you will first learn how to treat a beam-splitter in quantum optics, a very important tool that you need to know. You will also learn that when you want to describe an optical instrument in quantum optics, it is very useful to master its classical optics description. This lesson is an opportunity to think about the mysterious concept of wave-particle duality, and about the power of the quantum formalism, which can deal consistently with two behaviours apparently contradictory ....
Reading
6 vídeos (Total de 56 min), 3 leituras, 4 testes
Video6 videos
3.1 Beam-splitter in quantum optics16min
3.2 One photon wave-packet on a beam splitter9min
3.3 Mach-Zehnder interferometer in classical optics9min
3.4 One-photon interference5min
3.5 Wave-particle duality: “a quantum mystery”; a consistent formalism7min
Reading3 leituras
Homework 3min
Homework 3 correction30min
A historical feeble light interference experiment10min
Quiz4 exercícios práticos
Video 3.1 Tensor product properties6min
Video 3.2 Transforming photon number operator on a BS2min
Final practice quiz2min
Homework 3 evaluation20min

4

Seção
Clock
4 horas para concluir

Multimode quantized radiation: quantum optics in a real lab

In the real world there is nothing like purely monochromatic radiation. A correct description of radiation necessarily involves several modes. In this lesson, you will learn how canonical quantization can be easily generalized to the case of several modes, and how various observables or important quantities introduced in the single mode case are expressed in the multimode case. Beyond the formalism that you must learn to be able to read papers and books describing real situtations, you will encounter in this lesson some intriguing features of the quantum formalism: firstly, the unbelievably large size of the space of states, which is the reason for the unlimited potential power of quantum information; secondly, the question of infinities, a problem which was solved by the general procedure of renormalization. Note that optional readings are proposed as resources of some lectures....
Reading
8 vídeos (Total de 60 min), 3 leituras, 2 testes
Video8 videos
4.1 Canonical quantization of multimode radiation14min
4.2 Eigen-states of the Hamiltonian: space of states, energy of the vacuum7min
4.3 Total number of photons2min
4.4 Linear and angular momentum6min
4.5 Field observables: vacuum fluctuations4min
4.6 Photo-detection signals12min
4.7 Conclusion: what you have learned; the quantum vacuum7min
Reading3 leituras
Paper of Glauber 1983 on quantum formalism of light10min
Homework 430min
homework 4 corrected30min
Quiz2 exercícios práticos
Video 4.46min
Homework 4 evaluation22min

Instrutores

Alain Aspect

Professor
Physics

Michel Brune

Professor
Physics

Sobre École Polytechnique

L’École polytechnique associe recherche, enseignement et innovation au meilleur niveau scientifique et technologique mondial pour répondre aux défis du XXIe siècle. En tête des écoles d’ingénieur françaises depuis plus de 200 ans, sa formation promeut une culture d’excellence scientifique pluridisciplinaire, ouverte dans une forte tradition humaniste. ...

Perguntas Frequentes – FAQ

  • Once you enroll for a Certificate, you’ll have access to all videos, quizzes, and programming assignments (if applicable). Peer review assignments can only be submitted and reviewed once your session has begun. If you choose to explore the course without purchasing, you may not be able to access certain assignments.

  • When you purchase a Certificate you get access to all course materials, including graded assignments. Upon completing the course, your electronic Certificate will be added to your Accomplishments page - from there, you can print your Certificate or add it to your LinkedIn profile. If you only want to read and view the course content, you can audit the course for free.

  • There is no obligation, but the notions learned in this course will be necessary to follow the second course, which will present interaction between matter and quantized radiation, absorption, stimulated emission and spontaneous emission of photons, squeezed light, entangled photons, quantum treatment of non-linear optics, and applications to quantum technologies, etc...

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