About this Course
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Start instantly and learn at your own schedule.
Flexible deadlines

Flexible deadlines

Reset deadlines in accordance to your schedule.
Hours to complete

Approx. 29 hours to complete

Suggested: 7 weeks of study, 4-5 hours / week...
Available languages

English

Subtitles: English
100% online

100% online

Start instantly and learn at your own schedule.
Flexible deadlines

Flexible deadlines

Reset deadlines in accordance to your schedule.
Hours to complete

Approx. 29 hours to complete

Suggested: 7 weeks of study, 4-5 hours / week...
Available languages

English

Subtitles: English

Syllabus - What you will learn from this course

Week
1
Hours to complete
5 hours to complete

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 videos (Total 119 min), 3 readings, 10 quizzes
Video13 videos
1.0 Introduction to Lesson 15m
1.1 Canonical quantization10m
1.2.1 Material harmonic oscillator /111m
1.2.2 Material harmonic oscillator /212m
1.3 Single mode of radiation9m
1.4 Canonical quantization of a single mode10m
1.5 Observables6m
1.6 Number states; Photon7m
1.7 Vacuum fluctuations5m
1.8 What have we learnt? What next?4m
Introduction to homework 111m
Quantization of classical oscillators12m
Reading3 readings
Homework 1s
Correction of Homework 130m
Einstein's 1905 paper introducing the "photon"
Quiz10 practice exercises
Questions about the general introduction8m
Practice quiz video 1.110m
Practice quiz video 1.2.14m
Video 1.2.2.6m
Video 1.34m
Video 1.48m
Video 1.52m
Video 1.72m
Video 1.82m
Homework 1 evaluation16m
Week
2
Hours to complete
3 hours to complete

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 videos (Total 52 min), 2 readings, 5 quizzes
Video7 videos
2.1 The semi-classical model of optics9m
2.2 One-photon state in a single mode10m
2.3 Photo-detection signals7m
2.4 Single photo-detection signal for a one photon state4m
2.5 Double photo-detection signal for a one photon state: a fully quantum behavior6m
2.6 Quantum optics: a must9m
Reading2 readings
Homework 2s
Correction of Homework 230m
Quiz5 practice exercises
Video 2.14m
Video 2.22m
Video 2.32m
Video 2.68m
Homework 2 evaluation18m
Week
3
Hours to complete
3 hours to complete

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 videos (Total 56 min), 3 readings, 4 quizzes
Video6 videos
3.1 Beam-splitter in quantum optics16m
3.2 One photon wave-packet on a beam splitter9m
3.3 Mach-Zehnder interferometer in classical optics9m
3.4 One-photon interference5m
3.5 Wave-particle duality: “a quantum mystery”; a consistent formalism7m
Reading3 readings
Homework 3s
Homework 3 correction30m
A historical feeble light interference experiment10m
Quiz4 practice exercises
Video 3.1 Tensor product properties6m
Video 3.2 Transforming photon number operator on a BS2m
Final practice quiz2m
Homework 3 evaluation20m
Week
4
Hours to complete
4 hours to complete

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 videos (Total 60 min), 3 readings, 2 quizzes
Video8 videos
4.1 Canonical quantization of multimode radiation14m
4.2 Eigen-states of the Hamiltonian: space of states, energy of the vacuum7m
4.3 Total number of photons2m
4.4 Linear and angular momentum6m
4.5 Field observables: vacuum fluctuations4m
4.6 Photo-detection signals12m
4.7 Conclusion: what you have learned; the quantum vacuum7m
Reading3 readings
Paper of Glauber 1983 on quantum formalism of light10m
Homework 430m
homework 4 corrected30m
Quiz2 practice exercises
Video 4.46m
Homework 4 evaluation22m

Instructors

Avatar

Alain Aspect

Professor
Physics
Avatar

Michel Brune

Professor
Physics

About 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. ...

Frequently Asked Questions

  • 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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