oferecido por

École Polytechnique

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....

Comece imediatamente e aprenda em seu próprio cronograma.

Redefinir os prazos de acordo com sua programação.

Aprox. 28 horas restantes

Legendas: English

Comece imediatamente e aprenda em seu próprio cronograma.

Redefinir os prazos de acordo com sua programação.

Aprox. 28 horas restantes

Legendas: English

Seção

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....

13 vídeos (Total de 119 min), 3 leituras, 10 testes

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

Homework 1min

Correction of Homework 130min

Einstein's 1905 paper introducing the "photon"min

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

Seção

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....

7 vídeos (Total de 52 min), 2 leituras, 5 testes

2.0 Introduction4min

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

Homework 2min

Correction of Homework 230min

Video 2.14min

Video 2.22min

Video 2.32min

Video 2.68min

Homework 2 evaluation18min

Seção

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 ....

6 vídeos (Total de 56 min), 3 leituras, 4 testes

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

Homework 3min

Homework 3 correction30min

A historical feeble light interference experiment10min

Video 3.1 Tensor product properties6min

Video 3.2 Transforming photon number operator on a BS2min

Final practice quiz2min

Homework 3 evaluation20min

Seção

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....

8 vídeos (Total de 60 min), 3 leituras, 2 testes

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

Paper of Glauber 1983 on quantum formalism of light10min

Homework 430min

homework 4 corrected30min

Video 4.46min

Homework 4 evaluation22min

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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