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Quantum Optics 2 - Two photons and more
  • Level Foundation
  • Duration 13 hours
  • Course by École Polytechnique
  • Offered by

About

"Quantum Optics 1, Single photons", allowed learners to be introduced to the basic principles of light quantization, and to the standard formalism of Quantum Optics. All the examples were taken in single photons phenomena, including applications to quantum technologies. In the same spirit, "Quantum Optics 2, Two photons and more", will allow learners to use the Quantum Optics formalism to describe entangled photon, a unique feature at the root of the second quantum revolution and its applications to quantum technologies. Learners will also discover how the Quantum Optics formalism allows one to describe classical light, either coherent such as laser light, or incoherent such as thermal radiation. Using a many photons description, it is possible to derive the so-called Standard Quantum Limit (SQL), which applies to classical light, and to understand how new kinds of quantum states of light, such as squeezed states of light, allow one to beat the SQL, one of the achievements of quantum metrology. Several examples of Quantum Technologies based on entangled photons will be presented, firstly in quantum communication, in particular Quantum Teleportation and Quantum Cryptography. Quantum Computing and Quantum Simulation will also be presented, including some insights into the recently proposed Noisy Intermediate Scale Quantum (NISQ) computing, which raises a serious hope to demonstrate, in a near future, the actively searched quantum advantage, ie, the possibility to effect calculations exponentially faster than with classical computers.

Modules

Lesson 1 - Quasi-classical states of radiation: single mode case

    • 11 Videos
    • 2 Assignment
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2 Assignment

  • 1.6 Graded quiz
  • 1.10 Graded quiz

11 Videos

  • 1.0 Introduction
  • 1.1 Quantum Optics formalism in a nutshell
  • 1.2 Quasi-classical state: Definition and elementary properties
  • 1.3 Average field. Dispersion
  • 1.4 Photon number
  • 1.5 Photoelectric signals: fully classical
  • 1.6 Transformation on a beam splitter
  • 1.7 Single mode laser: an emblematic example
  • 1.8 Freely propagating beam: shot noise
  • 1.9 The standard shot noise formula: photocurrent fluctuations
  • 1.10 Conclusion: more than a classical macroscopic limit of quantum radiation

Homework 1: Quasi-classical states of radiation

    • 1 Readings
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1 Readings

  • Homework 1: Quasi-classical states of radiation

Lesson 2 - Multimode quasi-classical states of radiation

    • 8 Videos
    • 2 Assignment
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2 Assignment

  • 2.4 Graded quiz
  • 2.5 Graded Quiz

8 Videos

  • 2.0 Introduction
  • 2.1 Multimode quantum optics in a nutshell
  • 2.2 Multimode quasi-classical states: Poisson distribution of photons
  • 2.3 Quasi-classical wave packet; case of less than one photon
  • 2.4 Quasi-classical wave packet on a beam splitter
  • 2.5 Beat note between two laser beams; heterodyne detection
  • 2.6 Incoherent multimode radiation; classical vs quantum average
  • 2.7 Beyond classical light

Lesson 3 - Squeezed light: beating the standard quantum limit

    • 10 Videos
    • 1 Readings
    • 4 Assignment
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4 Assignment

  • 3.5 Graded Quiz
  • 3.6 Graded Quiz
  • 3.7 Graded quiz
  • 3.8 Graded quiz

10 Videos

  • 3.0 Introduction
  • 3.1 Balanced homodyne detection
  • 3.2 Quadrature components
  • 3.3 Complex plane representation: quadratures, field
  • 3.4 Squeezed state: definition, properties
  • 3.5 Measurements below the SQL
  • 3.6 Squeezing is fragile
  • 3.7 Beating the SQL in a Mach-Zehnder interferometer
  • 3.8 Beating the SQL in Gravitational Waves detection
  • 3.9 A genuine quantum technology

1 Readings

  • Carlton Caves first paper about squeezed light

Lesson 4 - Entanglement: a revolutionnary concept

    • 7 Videos
    • 4 Readings
    • 4 Assignment
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4 Assignment

  • 4.2 Graded Quiz
  • 4.3 Graded Quiz
  • 4.4 Graded Quiz
  • 4.5 Graded Quiz

7 Videos

  • 4.0 Introduction
  • 4.1 Polarized one photon wave packet: an almost ideal two-level system
  • 4.2 Pairs of photons entangled in polarization
  • 4.3 How to understand the EPR correlations?
  • 4.4 Bell’s inequalities: the possibility to settle the debate experimentally
  • 4.5 Experiments: local realism untenable
  • 4.6 Conclusion. Entanglement at the root of quantum technologies of the second quantum revolution

4 Readings

  • Bell 1964 paper on inequalities
  • AA 2001 Bell theorem: the naive view of an experimentalist
  • AA 2015 Closing the door
  • AA 2003 Bell foreword: the second quantum revolution

Lesson 5 - Entanglement based quantum technologies

    • 8 Videos
    • 3 Assignment
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3 Assignment

  • 5.1 Graded Quiz
  • 5.4 Graded Quiz
  • 5.5 Graded Quiz

8 Videos

  • 5.0 Introduction
  • 5.1 Quantum Key Distribution for cryptography: Ekert protocol
  • 5.2 QKD in the real world: need for quantum repeaters
  • 5.3 Bell states, Bell measurement: a basic tool in quantum information
  • 5.4 Quantum teleportation
  • 5.5 Quantum simulation
  • 5.6 Programmable quantum computing
  • 5.7 Conclusion: quantum optics at the heart of the second quantum revolution

Auto Summary

Explore the fascinating world of entangled photons and quantum technologies with "Quantum Optics 2 - Two photons and more." Led by expert instructors, this foundational course dives into advanced Quantum Optics, covering classical and quantum states of light, the Standard Quantum Limit, and cutting-edge applications in quantum communication, cryptography, and computing. Perfect for learners in Science & Engineering, the course spans 780 minutes and offers flexible Starter and Professional subscription options. Unlock the secrets of the second quantum revolution and gain insights into future technological advancements.

Alain Aspect
Instructors

Alain Aspect

Michel Brune
Instructors

Michel Brune