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.
Quantum Optics 1 : Single Photons
proposé par
École polytechnique
Programme du cours : ce que vous apprendrez dans ce cours
Semaine
1Quantization 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.
13 vidéos (Total 119 min), 3 lectures, 10 quiz
13 vidéos
1.0 Introduction to Lesson 15 min
1.1 Canonical quantization10 min
1.2.1 Material harmonic oscillator /111 min
1.2.2 Material harmonic oscillator /212 min
1.3 Single mode of radiation9 min
1.4 Canonical quantization of a single mode10 min
1.5 Observables6 min
1.6 Number states; Photon7 min
1.7 Vacuum fluctuations5 min
1.8 What have we learnt? What next?4 min
Introduction to homework 111 min
Quantization of classical oscillators12 min
3 lectures
Homework 1s
Correction of Homework 130 min
Einstein's 1905 paper introducing the "photon"
10 exercices pour s'entraîner
Questions about the general introduction8 min
Practice quiz video 1.110 min
Practice quiz video 1.2.14 min
Video 1.2.2.6 min
Video 1.34 min
Video 1.48 min
Video 1.52 min
Video 1.72 min
Video 1.82 min
Homework 1 evaluation16 min
Semaine
2One 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.
7 vidéos (Total 52 min), 2 lectures, 5 quiz
7 vidéos
2.0 Introduction4 min
2.1 The semi-classical model of optics9 min
2.2 One-photon state in a single mode10 min
2.3 Photo-detection signals7 min
2.4 Single photo-detection signal for a one photon state4 min
2.5 Double photo-detection signal for a one photon state: a fully quantum behavior6 min
2.6 Quantum optics: a must9 min
2 lectures
Homework 2s
Correction of Homework 230 min
5 exercices pour s'entraîner
Video 2.14 min
Video 2.22 min
Video 2.32 min
Video 2.68 min
Homework 2 evaluation18 min
Semaine
3One 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 .
6 vidéos (Total 56 min), 3 lectures, 4 quiz
6 vidéos
3.1 Beam-splitter in quantum optics16 min
3.2 One photon wave-packet on a beam splitter9 min
3.3 Mach-Zehnder interferometer in classical optics9 min
3.4 One-photon interference5 min
3.5 Wave-particle duality: “a quantum mystery”; a consistent formalism7 min
3 lectures
Homework 3s
Homework 3 correction30 min
A historical feeble light interference experiment10 min
4 exercices pour s'entraîner
Video 3.1 Tensor product properties6 min
Video 3.2 Transforming photon number operator on a BS2 min
Final practice quiz2 min
Homework 3 evaluation20 min
Semaine
4Multimode 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.
8 vidéos (Total 60 min), 3 lectures, 2 quiz
8 vidéos
4.1 Canonical quantization of multimode radiation14 min
4.2 Eigen-states of the Hamiltonian: space of states, energy of the vacuum7 min
4.3 Total number of photons2 min
4.4 Linear and angular momentum6 min
4.5 Field observables: vacuum fluctuations4 min
4.6 Photo-detection signals12 min
4.7 Conclusion: what you have learned; the quantum vacuum7 min
3 lectures
Paper of Glauber 1983 on quantum formalism of light10 min
Homework 430 min
homework 4 corrected30 min
2 exercices pour s'entraîner
Video 4.46 min
Homework 4 evaluation22 min
Enseignants
Alain Aspect
ProfessorPhysics
Michel Brune
ProfessorPhysics
À propos de 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.
Foire Aux Questions
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Quelle est la politique de remboursement ?
Une aide financière est-elle possible ?
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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