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...

oferecido por

## Quantum Optics 1 : Single Photons

## Informações sobre o curso

### Resultados de carreira do aprendiz

## 50%

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### Resultados de carreira do aprendiz

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## 20%

#### 100% on-line

#### Prazos flexíveis

#### Aprox. 23 horas para completar

#### Inglês

## Programa - O que você aprenderá com este curso

**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.

**5 horas para concluir**

**13 videos**

**3 leituras**

**10 exercícios práticos**

**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.

**3 horas para concluir**

**7 videos**

**2 leituras**

**5 exercícios práticos**

**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 .

**3 horas para concluir**

**6 videos**

**3 leituras**

**4 exercícios práticos**

**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.

**4 horas para concluir**

**8 videos**

**3 leituras**

**2 exercícios práticos**

### Avaliações

##### Principais avaliações do QUANTUM OPTICS 1 : SINGLE PHOTONS

Very clear and informative. The courses are short respectively and they are very exciting. The quizzes are a very good review to keep you concentrated.

There should be more resources to study like some lecture notes. Besides that, the overall level is very good.

This course give me a brief idea about single photon. Thank you for providing such a good course.

A course worth taking for those seeking an introduction to Quantum Optics.

Can't wait any longer for the second course. Wonderful. Stimulating.

Great Course! Thinking about taking the second part of this series.

A. Aspect is clear methodical and precise. It makes learning eas

### oferecido por

#### 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

Quando terei acesso às palestras e às tarefas?

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O que recebo ao adquirir o Certificado?

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Qual é a política de reembolso?

Existe algum auxílio financeiro disponível?

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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