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# QUANTUM OPTICS: SINGLE PHOTON

Start

10/28/2019

Duration

7 weeks

Rhythm

4 - 5 h/week

Prerequisites

Undergraduate knowledge of quantum mechanics and classical electromagnetism. Course on demand.

Discipline

Physics

Course language

English

PRESENTATION:

For a long time, it was thought that light could be fully described as a classical electromagnetic wave obeying Maxwell's equations. In the last decades, however, it became possible to produce new states of light with unprecedented properties, impossible to understand in the context of classical electromagnetism, and demanding the use of the quantum optics formalism. This course will introduce many basic tools of the quantum optics formalism, and use them to describe an emblematic example of fully quantum states of light: one-photon wave-packets. These tools will be also used in the follow up of this course, which will present entangled pairs of photons, squeezed states of light, interaction of quantized light with matter, and their applications to quantum technologies. Behave both as a wave and a particle, and/or how to use it in quantum technologies, embark with us!

ABOUT THE COURSE

In order to obtain the formalism of quantum optics, one must start from classical Maxwell's equations, and quantize them. One can then use the general formalism of quantum mechanics, with some adaptation. In order to benefit from the course, it is thus necessary to have some knowledge of classical electromagnetism, and of standard quantum mechanics. The course can then be considered as an advanced undergraduate course.

Quantum optics phenomena are fascinating, and the central theme of this course, wave-particle duality for a single particle (here a single photon) was declared by Richard Feynman “the great mystery” of quantum mechanics, in his famous Lectures on physics (volume III, chapter 1). The great physicist then added: ‘We cannot make the mystery go away by “explaining” how it works. We will just tell you how it works.” This is one of the goals of this MOOC, helping you to get a better understanding of quantum optics by learning how it works.

But there is another big interest in quantum optics. It turns out that quantum optics is one of the key components of the quantum technologies, which are a result of the ongoing second quantum revolution. One-photon sources play a very important role in these quantum technologies.

If you want to understand what is a photon, how it can behave both as a wave and a particle, and/or how to use it in quantum technologies, embark with us!

COURSE SYLLABUS

Week 1 : Quantization of free radiation: one mode

Canonical quantization

Material harmonic oscillator

Single mode of radiation

Canonical quantization of a single mode

Observables

Number states, photon

Vacuum fluctuations

Homework 1: quantization of a standing wave in a cavity

Week 2 : One photon in a single mode: particle-like behavior

The semi-classical model of optics

One photon in a single mode

Photo-detection signals

Single photo-detection signal for one photon

Double photo-detection signal for one photon: a fully quantum behavior

Quantum optics: a must

Homework 2: The "coherent states" of light

Week 3 : One photon interferences: Wave-particle duality

Beam-splitter in quantum optics

One photon on a beam splitter

Mach-Zehnder interferometer in classical optics

One-photon interference

Wave-particle duality: a quantum mystery; a consistent formalism

Homework 3: Field state transformation on a beamsplitter

Week 4 : Multimode quantized radiation: quantum optics in a real laboratory

Canonical quantization of multimode radiation

Eigenstates of the Hamiltonian; energy of the vacuum

Total number of photons

Linear and angular momentum of a photon

Field observables; vacuum fluctuations

Photo-detection signals

Homework 4: Multimode radiation field states: localized single photon state

Week 5 : One-photon sources in the real world

Heisenberg formalism; photo detection signals

Multimode one-photon wave packet

Spontaneous emission photon

A detour to Fourier transforms

Real one-photon sources

One-photon sources for what?

Homework 5: Generation of photon pairs by parametric down conversion

Week 6 : Wave-particle duality for a single photon in the real world

Anti-correlation on a beam splitter

Anti-correlation experiments

Supplementary photons

One-photon interference: formalism

One-photon interference: experiments

Wave-particle duality and complementarity

A fruitful mystery

Homework 6: Shot-noise limit of interferometry

Week 7 : One photon based quantum technologies

Quantum Random Number Generator (QRNG)

Weak light pulses on a beam splitter

One photon polarization as a qubit

Quantum cryptography: the BB84 scheme

The no-cloning theorem

Conclusion and outlook

SUGGESTED READINGS

The lectures are self-contained, but the learners will find useful additional information in the following book: G. Grynberg, Alain Aspect and Claude Fabre: Introduction to quantum optics, Cambridge University Press (2010).LIEN : https://www.cambridge.org/fr/academic/subjects/physics/optics-optoelect…

Teacher(s)