About this course: 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.
Who is this class for: This course is primarily intended for university students who have a good knowledge of basic quantum mechanics and classical electromagnetism, and who want to enter in the field of quantum optics. It is also intended for engineers who want to catch up with the rapidly developing quantum technologies derived from the second quantum revolution, in which the observation and control of single quantum objects, such as single photons, is a key ingredient.
Created by: École Polytechnique
Taught by: Alain Aspect, Professor
Physics
Taught by: Michel Brune, Professor
Physics
| Commitment | 7 weeks of study, 4-5 hours / week |
| Language | English |
| How To Pass | Pass all graded assignments to complete the course. |
| User Ratings |
Syllabus
WEEK 1
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.
13 videos, 3 readings, 9 practice quizzes
- Video: 0.0 General introduction to the course
- Practice Quiz: Questions about the general introduction
- Video: 1.0 Introduction to Lesson 1
- Video: 1.1 Canonical quantization
- Practice Quiz: Practice quiz video 1.1
- Video: 1.2.1 Material harmonic oscillator /1
- Practice Quiz: Practice quiz video 1.2.1
- Video: 1.2.2 Material harmonic oscillator /2
- Practice Quiz: Video 1.2.2.
- Video: 1.3 Single mode of radiation
- Practice Quiz: Video 1.3
- Video: 1.4 Canonical quantization of a single mode
- Practice Quiz: Video 1.4
- Video: 1.5 Observables
- Practice Quiz: Video 1.5
- Video: 1.6 Number states; Photon
- Video: 1.7 Vacuum fluctuations
- Practice Quiz: Video 1.7
- Video: 1.8 What have we learnt? What next?
- Practice Quiz: Video 1.8
- Video: Introduction to homework 1
- Reading: Homework 1
- Reading: Correction of Homework 1
- Video: Quantization of classical oscillators
- Reading: Einstein's 1905 paper introducing the "photon"
Graded: Homework 1 evaluation
WEEK 2
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.
7 videos, 2 readings, 4 practice quizzes
- Video: 2.0 Introduction
- Video: 2.1 The semi-classical model of optics
- Practice Quiz: Video 2.1
- Video: 2.2 One-photon state in a single mode
- Practice Quiz: Video 2.2
- Video: 2.3 Photo-detection signals
- Practice Quiz: Video 2.3
- Video: 2.4 Single photo-detection signal for a one photon state
- Video: 2.5 Double photo-detection signal for a one photon state: a fully quantum behavior
- Video: 2.6 Quantum optics: a must
- Practice Quiz: Video 2.6
- Reading: Homework 2
- Reading: Correction of Homework 2
Graded: Homework 2 evaluation
WEEK 3
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 .
6 videos, 3 readings, 3 practice quizzes
- Video: 3.0 Introduction to Lesson 3
- Video: 3.1 Beam-splitter in quantum optics
- Practice Quiz: Video 3.1 Tensor product properties
- Video: 3.2 One photon wave-packet on a beam splitter
- Practice Quiz: Video 3.2 Transforming photon number operator on a BS
- Video: 3.3 Mach-Zehnder interferometer in classical optics
- Video: 3.4 One-photon interference
- Video: 3.5 Wave-particle duality: “a quantum mystery”; a consistent formalism
- Practice Quiz: Final practice quiz
- Reading: Homework 3
- Reading: Homework 3 correction
- Reading: A historical feeble light interference experiment
Graded: Homework 3 evaluation
WEEK 4
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.
8 videos, 3 readings, 1 practice quiz
- Video: 4.0 Introduction to lesson 4
- Video: 4.1 Canonical quantization of multimode radiation
- Video: 4.2 Eigen-states of the Hamiltonian: space of states, energy of the vacuum
- Video: 4.3 Total number of photons
- Video: 4.4 Linear and angular momentum
- Practice Quiz: Video 4.4
- Video: 4.5 Field observables: vacuum fluctuations
- Video: 4.6 Photo-detection signals
- Video: 4.7 Conclusion: what you have learned; the quantum vacuum
- Reading: Paper of Glauber 1983 on quantum formalism of light
- Reading: Homework 4
- Reading: homework 4 corrected
Graded: Homework 4 evaluation
WEEK 5
One photon sources in the real world
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.
7 videos, 2 readings
- Video: 5.0 Introduction to Lesson 5
- Video: 5.1 Heisenberg formalism: photo-detection signals
- Video: 5.2 Multimode one-photon wave-packet
- Video: 5.3 Spontaneous emission photon
- Video: 5.4 A detour to Fourier transforms
- Video: 5.5 Real one-photon sources
- Video: 5.6 One-photon sources for what?
- Reading: Homework 5
- Reading: Homework 5 corrected
Graded: Evaluation of homework 5
WEEK 6
Wave-particle duality for a single photon in the real world
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.
8 videos, 2 readings, 1 practice quiz
- Video: 6.0 Introduction to Lesson 6
- Video: 6.1 Anti-correlation for a one-photon wave-packet on a beam-splitter
- Video: 6.2 Anti-correlation experiments: fully quantum behavior
- Video: 6.3 Anti-correlation with supplementary photons
- Video: 6.4 One-photon interference signal
- Practice Quiz: video 6.4
- Video: 6.5 One photon interference experiment
- Video: 6.6 Wave particle duality and complementarity
- Video: 6.7 A fruitful mystery
- Reading: Homework 6
- Reading: Correction of homework 6
Graded: Evaluation of homework 6
WEEK 7
One-photon based quantum technologies
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.
7 videos, 1 reading, 2 practice quizzes
- Video: 7.0 The second quantum revolution: from concepts to technology
- Video: 7.1 Quantum random numbers generator (QRNG)
- Practice Quiz: Video 7.1
- Video: 7.2 Weak light pulses on a beam-splitter
- Video: 7.3 One-photon polarization as a qubit
- Video: 7.4 Quantum cryptography: the BB84 QKD scheme
- Video: 7.5 The no-cloning theorem
- Video: 7.6 Conclusion of the lesson and of Quantum Optics 1
- Reading: Homework 7
- Practice Quiz: Evaluation of homework 7 (non graded)
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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.
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Ratings and Reviews
More exact usage of English language would help. Also written course material would be great. I ended up buying Mr. Aspect's book because I like the topic so much. A final exam would give a more satisfying feeling. I have the feeling I muddled through on lots of the questions. I am redoing the course now to get "perfect" understanding an memorizing things. Alternatively, a final test could be to write a reaction about a resent article.
This is a first rate course given by a master of the subject matter. The presentation style - especially for the equations - are easy to follow. The ideas and concepts are concisely explained. The enthusiasm is infectious. I would recommend it to anyone who wants to know the latest developments in quantum optics. I look forward to part 2!
A course worth taking for those seeking an introduction to Quantum Optics.
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A. Aspect is clear methodical and precise. It makes learning eas