Quantum Optics 1 : Single Photons
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.
Monthly Subscription Starting at AED 99 + VAT
- Level Foundation
- Duration 33 hours
- Course by École Polytechnique
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Offered by
About
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.Modules
General introduction to the course
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1
Videos
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1
Assignment
1
Assignment
- Questions about the general introduction
1
Videos
- 0.0 General introduction to the course
Lesson 1: Quantization of free radiation: one mode
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10
Videos
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8
Assignment
8
Assignment
- Practice quiz video 1.1
- Practice quiz video 1.2.1
- Video 1.2.2.
- Video 1.3
- Video 1.4
- Video 1.5
- Video 1.7
- Video 1.8
10
Videos
- 1.0 Introduction to Lesson 1
- 1.1 Canonical quantization
- 1.2.1 Material harmonic oscillator /1
- 1.2.2 Material harmonic oscillator /2
- 1.3 Single mode of radiation
- 1.4 Canonical quantization of a single mode
- 1.5 Observables
- 1.6 Number states; Photon
- 1.7 Vacuum fluctuations
- 1.8 What have we learnt? What next?
Homework 1: quantization of a standing wave in a cavity
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2
Videos
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2
Readings
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1
Assignment
1
Assignment
- Homework 1 evaluation
2
Videos
- Introduction to homework 1
- Quantization of classical oscillators
2
Readings
- Homework 1
- Correction of Homework 1
Lecture 1. Complementary documents
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1
Readings
1
Readings
- Einstein's 1905 paper introducing the "photon"
Lesson 2. One photon state in a single mode: particle-like behaviour
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7
Videos
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4
Assignment
4
Assignment
- Video 2.1
- Video 2.2
- Video 2.3
- Video 2.6
7
Videos
- 2.0 Introduction
- 2.1 The semi-classical model of optics
- 2.2 One-photon state in a single mode
- 2.3 Photo-detection signals
- 2.4 Single photo-detection signal for a one photon state
- 2.5 Double photo-detection signal for a one photon state: a fully quantum behavior
- 2.6 Quantum optics: a must
Homework 2: The "coherent states" of light
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2
Readings
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1
Assignment
1
Assignment
- Homework 2 evaluation
2
Readings
- Homework 2
- Correction of Homework 2
Lesson 3. One photon interference: Wave-Particle duality
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6
Videos
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3
Assignment
3
Assignment
- Video 3.1 Tensor product properties
- Video 3.2 Transforming photon number operator on a BS
- Final practice quiz
6
Videos
- 3.0 Introduction to Lesson 3
- 3.1 Beam-splitter in quantum optics
- 3.2 One photon wave-packet on a beam splitter
- 3.3 Mach-Zehnder interferometer in classical optics
- 3.4 One-photon interference
- 3.5 Wave-particle duality: “a quantum mystery”; a consistent formalism
Homework 3: Field state transformation on a beamsplitter
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2
Readings
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1
Assignment
1
Assignment
- Homework 3 evaluation
2
Readings
- Homework 3
- Homework 3 correction
Lesson 3: Complementary documents
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1
Readings
1
Readings
- A historical feeble light interference experiment
Lesson 4 - Multimode quantized radiation: quantum optics in a real lab
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8
Videos
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1
Readings
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1
Assignment
1
Assignment
- Video 4.4
8
Videos
- 4.0 Introduction to lesson 4
- 4.1 Canonical quantization of multimode radiation
- 4.2 Eigen-states of the Hamiltonian: space of states, energy of the vacuum
- 4.3 Total number of photons
- 4.4 Linear and angular momentum
- 4.5 Field observables: vacuum fluctuations
- 4.6 Photo-detection signals
- 4.7 Conclusion: what you have learned; the quantum vacuum
1
Readings
- Paper of Glauber 1983 on quantum formalism of light
Homework 4: Multimode radiation field states: localized single photon state
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2
Readings
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1
Assignment
1
Assignment
- Homework 4 evaluation
2
Readings
- Homework 4
- homework 4 corrected
Lesson 5 - One photon sources in the real world
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7
Videos
7
Videos
- 5.0 Introduction to Lesson 5
- 5.1 Heisenberg formalism: photo-detection signals
- 5.2 Multimode one-photon wave-packet
- 5.3 Spontaneous emission photon
- 5.4 A detour to Fourier transforms
- 5.5 Real one-photon sources
- 5.6 One-photon sources for what?
Homework 5: Generation of photon pairs by parametric down conversion
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2
Readings
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1
Assignment
1
Assignment
- Evaluation of homework 5
2
Readings
- Homework 5
- Homework 5 corrected
Lesson 6 Wave-particle duality for a single photon in the real world
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8
Videos
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1
Assignment
1
Assignment
- video 6.4
8
Videos
- 6.0 Introduction to Lesson 6
- 6.1 Anti-correlation for a one-photon wave-packet on a beam-splitter
- 6.2 Anti-correlation experiments: fully quantum behavior
- 6.3 Anti-correlation with supplementary photons
- 6.4 One-photon interference signal
- 6.5 One photon interference experiment
- 6.6 Wave particle duality and complementarity
- 6.7 A fruitful mystery
Homework 6: Shot-noise limit of interferometry
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2
Readings
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1
Assignment
1
Assignment
- Evaluation of homework 6
2
Readings
- Homework 6
- Correction of homework 6
Lesson 7. One-photon based quantum technologies
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7
Videos
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1
Assignment
1
Assignment
- Video 7.1
7
Videos
- 7.0 The second quantum revolution: from concepts to technology
- 7.1 Quantum random numbers generator (QRNG)
- 7.2 Weak light pulses on a beam-splitter
- 7.3 One-photon polarization as a qubit
- 7.4 Quantum cryptography: the BB84 QKD scheme
- 7.5 The no-cloning theorem
- 7.6 Conclusion of the lesson and of Quantum Optics 1
Homework 7
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1
Readings
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1
Assignment
1
Assignment
- Evaluation of homework 7 (non graded)
1
Readings
- Homework 7
Auto Summary
Explore the fascinating world of quantum optics with "Quantum Optics 1: Single Photons." This foundational course, led by Coursera, delves into the quantization of light, quantum states, and wave-particle duality. Ideal for those with a background in quantum mechanics and classical electromagnetism, it covers essential tools and concepts for understanding modern quantum optics and its applications in emerging quantum technologies. With a duration of 1980 minutes, the course is available through Starter and Professional subscription options. Perfect for science and engineering enthusiasts seeking to deepen their knowledge in this intriguing domain.
Alain Aspect
Michel Brune