Quantum Optics 1 : Single Photons

所在平台: Coursera

课程主页: https://www.coursera.org/learn/quantum-optics-single-photon

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课程简介

课程名称：量子光学 1：单光子 课程概述：本课程将提供基本工具和概念，以帮助您理解现代量子光学的研究文章和书籍。您将学习光的量子化、描述光的量子态的形式主义（无任何经典对应物）以及可观察量，从而展示这些状态的典型量子特性。课程将应用于单光子波包这一典型案例，展示其既可以表现为粒子又可以表现为波的特性。理查德·费曼曾称波粒二象性为伟大的量子谜题。您将能够完全欣赏展示单光子波粒二象性的真实实验，以及基于单光子源的量子技术应用，这些技术目前已经商业化。课程中介绍的工具将在我们的第二门量子光学课程中广泛应用，该课程将介绍更高级的话题，例如纠缠、量子光与物质的相互作用、压缩光等。 如果您对基础量子力学和经典电磁学有良好的知识基础，但一直想了解： - 如何从经典电磁学过渡到量子化辐射， - 光子的概念是如何出现的， - 统一的形式主义如何能够描述量子光学实验中观察到的看似矛盾的行为， - 创造性的物理学家和工程师如何基于光的量子特性发明全新的技术， 那么这门课程适合您。 课程大纲： 1. **光的量子化：一种模式** 学习规范量子化，应用于电磁场的单一模式量子化，并发现其表现为量子谐振子。 2. **单模式中的单光子状态：粒子行为** 了解量子光学形式主义如何导致单光子波包的粒子行为，学习量子光学中简单和联合光子探测信号的表达。 3. **单光子干涉：波粒二象性** 探讨单光子如何自我干涉，计算在马赫-曾德干涉仪中发射单光子的干涉图样。 4. **多模量子辐射：真实实验室中的量子光学** 介绍如何将规范量子化推广到多个模式，以及在多模式情况下所引入的重要观测量。 5. **现实中的单光子源** 讨论现代各种单光子源，包括呼唤光子源和按需光子源，学习如何描述自发发射光子的波包。 6. **现实世界中的单光子波粒二象性** 开展真实实验的描述，揭示单光子波包的双重特性。 7. **基于单光子的量子技术** 探索以单光子源为基础的两种量子技术，例如量子密码学和量子随机数生成器，以及它们与传统技术的区别。 此课程将使您具备理解和应用量子光学的能力，并为进一步的研究奠定基础。

课程大纲

Part: 1

Title:Quantization of light: one mode

Description: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.

Part: 2

Title:One photon state in a single mode: particle-like behaviour

Description: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.

Part: 3

Title:One photon interference: Wave-Particle duality

Description: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 .

Part: 4

Title:Multimode quantized radiation: quantum optics in a real lab

Description: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.

Part: 5

Title:One photon sources in the real world

Description:One photon sources are important components in quantum optics, both in research laboratories and in applied quantum technologies. The lesson of this week will present the various kinds of one-photon sources available today, from heralded one photon sources to one photon sources on demand. You will learn how to use the multimode formalism presented in a previous lesson, to describe one-photon wave packets, in particular in the case of a spontaneously emitted photon. You will start with the presentation of a theoretical tool much used in quantum optics, the Heisenberg formalism. It will allow you to discover the formula expressing the probability of a double detection at two different times. You will also learn some `tricks of the trade' about Fourier transforms.

Part: 6

Title:Wave-particle duality for a single photon in the real world

Description:You are now ready to develop the description of a real experiment , which was the first one to reveal directly the dual nature -- wave and particle, of a real single photon wave-packet. You will not only be able to describe, with the formalism you have learned, both the particle-like and the wave-like behaviors, but you will also see how to take into account the features of a real experiment, which is never perfect. Last and not least, we will have the opportunity to think about the notions of wave-particle duality and complementarity, which should be not confused, and about thethe statement of Feynman, who named wave-particle duality “a great quantum mystery”. I will try to convince you that when one identifies a mysterious behavior, one should not complain, but rather explore the possibility that something new and interesting can emerge from that mystery.

Part: 7

Title:One-photon based quantum technologies

Description:In this lesson, you will discover two quantum technologies based on one photon sources. Quantum technologies allow one to achieve a goal in a way qualitatively different from a classical technology aiming at the same goal. For instance, quantum cryptography is immune to progress in computers power, while many classical cryptography methods can in principle be broken when we have more powerful computers. Similarly, quantum random number generators yield true random numbers, while classical random number generators only produce pseudo-random numbers, which might be guessed by somebody else than the user. This lesson is also an opportunity to learn two important concepts in quantum information: (i) qubits based on photon polarization; (ii) the celebrated no-cloning theorem, at the root of the security of quantum cryptography.

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