Offered By

École Polytechnique

About this Course

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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.

Start instantly and learn at your own schedule.

Reset deadlines in accordance to your schedule.

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

Subtitles: English...

Start instantly and learn at your own schedule.

Reset deadlines in accordance to your schedule.

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

Subtitles: English...

Week

1In 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....

13 videos (Total 119 min), 3 readings, 10 quizzes

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

Homework 1m

Correction of Homework 130m

Einstein's 1905 paper introducing the "photon"m

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

2In 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....

7 videos (Total 52 min), 2 readings, 5 quizzes

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

Homework 2m

Correction of Homework 230m

Video 2.14m

Video 2.22m

Video 2.32m

Video 2.68m

Homework 2 evaluation18m

Week

3In 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 ....

6 videos (Total 56 min), 3 readings, 4 quizzes

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

Homework 3m

Homework 3 correction30m

A historical feeble light interference experiment10m

Video 3.1 Tensor product properties6m

Video 3.2 Transforming photon number operator on a BS2m

Final practice quiz2m

Homework 3 evaluation20m

Week

4In 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....

8 videos (Total 60 min), 3 readings, 2 quizzes

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

Paper of Glauber 1983 on quantum formalism of light10m

Homework 430m

homework 4 corrected30m

Video 4.46m

Homework 4 evaluation22m

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.
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When will I have access to the lectures and assignments?

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.

What will I get if I purchase the Certificate?

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.

What is the refund policy?

Is financial aid available?

Is it necessary to follow this course to enrol in the future second course on quantum optics?

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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