1.0 Introduction to Lesson 1

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来自 École Polytechnique 的课程

Quantum Optics 1 : Single Photons

63 个评分

École Polytechnique

Quantum Optics 1 : Single Photons

63 个评分

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.

从本节课中

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.

1.0 Introduction to Lesson 15:01

1.1 Canonical quantization10:28

1.2.1 Material harmonic oscillator /111:29

1.2.2 Material harmonic oscillator /212:01

1.3 Single mode of radiation9:51

1.4 Canonical quantization of a single mode10:26

1.5 Observables6:54

1.6 Number states; Photon7:08

1.7 Vacuum fluctuations5:26

1.8 What have we learnt? What next?4:42

与讲师见面

Alain Aspect
Professor
Physics
Michel Brune
Professor
Physics

Welcome to the first lesson of this introductory course on quantum optics.

In this lesson, you will discover how it is possible to quantize

the electromagnetic field starting from classical Maxwell's Equations and

using a method known as canonical quantization.

We will consider today the case where the field is far from the sources,

that is to say free radiation.

Moreover, we will effect the quantization for a single mode,

leaving the multi-mode case for a future lesson.

Even for a single mode,

the canonical quantization of the electromagnetic field is not simple.

But if you make the effort to follow me, you will be rewarded.

You will know where the formalism that we will use all along the course comes from.

When I started reading quantum optics papers,

I had to accept that formalism without justification.

And I was frustrated until the moment when I found the presentation of the reasoning

leading to the equations that we use all the time in quantum optics.

I would like to avoid that frustration to those of you who like me,

want to know where the formalism comes from.

I know that not everybody is the same.

And you may be mostly interested in learning how the formalism works

in order to apply it to the wonders of quantum optics.

Even if it is your case do not skip this lesson since we will introduce

many notions that will be very important in the rest of the course.

Let us look together at the summary of the lesson and

I will tell you what you might skip.

In the first section,

I will explain the general method to quantize any classical system.

You may decide to skip this.

In the second section, you will first apply the general method

to the quantization of a classical, mechanical, harmonic oscillator.

You may want to skip the beginning of that part.

But as soon as you hear of Dirac formalism, it is time to listen carefully

since Dirac formalism is used all the time in quantum optics.

After a pause, we will continue our survey of the quantization

of the mechanical harmonic oscillator.

It will allow me to introduce many notions that will be useful for the whole course.

In particular, do not miss the explanations about energy levels,

number states, and quantum fluctuations.

In section three, you will find the definition of a classical mode

of radiation, a notion essential in quantum optics.

In section four, you will discover that radiation in a classical mode,

can be quantized exactly as a classical harmonic oscillator.

This will allow us to jump directly into the full formalism of quantum optics.

As usual, in quantum mechanics,

we must define the quantum observables associated with measurable quantities.

This will be done in section five.

In section six, you will discover how the properties of the eigenstates

of the Hamiltonian allow us to define the notion of photon,

one of the landmarks of quantum optics.

Another important consequence of quantization

is the existence of vacuum fluctuations.

Fluctuation of the vacuum may be an oxymoron in the classical world but it is

a fact in quantum physics with important consequences which can be observed.

This first lesson I must admit is a little too long.

However, it would have been frustrating to split it in two parts

since the exciting matter is in the second part.

But do not panic, future lessons will be shorter.

And now embark with me into quantization of radiation.

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