Quantum Optics 1 : Single Photons
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Quantum Optics 1 : Single Photons
École Polytechnique
课程信息
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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.
教学大纲 - 您将从这门课程中学到什么
Week
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 个视频（共 119 分钟）, 3 个阅读材料, 10 个测验
13 个视频
1.0 Introduction to Lesson 15分钟
1.1 Canonical quantization10分钟
1.2.1 Material harmonic oscillator /111分钟
1.2.2 Material harmonic oscillator /212分钟
1.3 Single mode of radiation9分钟
1.4 Canonical quantization of a single mode10分钟
1.5 Observables6分钟
1.6 Number states; Photon7分钟
1.7 Vacuum fluctuations5分钟
1.8 What have we learnt? What next?4分钟
Introduction to homework 111分钟
Quantization of classical oscillators12分钟
3 个阅读材料
Homework 1分钟
Correction of Homework 130分钟
Einstein's 1905 paper introducing the "photon"分钟
10 个练习
Questions about the general introduction8分钟
Practice quiz video 1.110分钟
Practice quiz video 1.2.14分钟
Video 1.2.2.6分钟
Video 1.34分钟
Video 1.48分钟
Video 1.52分钟
Video 1.72分钟
Video 1.82分钟
Homework 1 evaluation16分钟
Week
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 个视频（共 52 分钟）, 2 个阅读材料, 5 个测验
7 个视频
2.1 The semi-classical model of optics9分钟
2.2 One-photon state in a single mode10分钟
2.3 Photo-detection signals7分钟
2.4 Single photo-detection signal for a one photon state4分钟
2.5 Double photo-detection signal for a one photon state: a fully quantum behavior6分钟
2.6 Quantum optics: a must9分钟
2 个阅读材料
Homework 2分钟
Correction of Homework 230分钟
5 个练习
Video 2.14分钟
Video 2.22分钟
Video 2.32分钟
Video 2.68分钟
Homework 2 evaluation18分钟
Week
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 个视频（共 56 分钟）, 3 个阅读材料, 4 个测验
6 个视频
3.1 Beam-splitter in quantum optics16分钟
3.2 One photon wave-packet on a beam splitter9分钟
3.3 Mach-Zehnder interferometer in classical optics9分钟
3.4 One-photon interference5分钟
3.5 Wave-particle duality: “a quantum mystery”; a consistent formalism7分钟
3 个阅读材料
Homework 3分钟
Homework 3 correction30分钟
A historical feeble light interference experiment10分钟
4 个练习
Video 3.1 Tensor product properties6分钟
Video 3.2 Transforming photon number operator on a BS2分钟
Final practice quiz2分钟
Homework 3 evaluation20分钟
Week
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 个视频（共 60 分钟）, 3 个阅读材料, 2 个测验
8 个视频
4.1 Canonical quantization of multimode radiation14分钟
4.2 Eigen-states of the Hamiltonian: space of states, energy of the vacuum7分钟
4.3 Total number of photons2分钟
4.4 Linear and angular momentum6分钟
4.5 Field observables: vacuum fluctuations4分钟
4.6 Photo-detection signals12分钟
4.7 Conclusion: what you have learned; the quantum vacuum7分钟
3 个阅读材料
Paper of Glauber 1983 on quantum formalism of light10分钟
Homework 430分钟
homework 4 corrected30分钟
2 个练习
Video 4.46分钟
Homework 4 evaluation22分钟
讲师
Alain Aspect
ProfessorPhysics
Michel Brune
ProfessorPhysics
关于 École Polytechnique
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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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