Hi, nice to have you with us. I am Alain Aspect with my colleague, Michel Brune. We have prepared for you this first course on quantum optics centered on quantized light, and some of its extraordinary properties. Before embarking into this course you may ask the question, why quantize light? According to the basic principles of physics, everything should be described in the framework of quantum mechanics, and light is not an exception. So the first reason to learn quantization of light is a matter of principle. But we know that in practice it often happens that one does not need to resort to a quantum description of physics phenomena. For instance, if you want to describe the motion of planets around the sun, you don't use Schrodinger equation, you use Newton's mechanics. So, I can rephrase the question, do we really need to quantized light? Until the 1970s, the answer was not 100% yes. Almost all known phenomena of optics could be described in the framework of classical electromagnetism. That is to say, light could be described as a classical electromagnetic wave, obeying Maxwell's equations, without any reference to the notion of photon. Quantum mechanics was needed only to describe matter. Completed with the Hamiltonian describing the interaction between classical radiation and quantized matter, you get the semi-classical model of optics. This model describes successfully most optics phenomena. Such as, free propagation, interference, diffraction. It also describes successfully absorption and stimulated emission of light by matter. This is enough to understand laser physics as shown in the first part of our book on quantum optics. [MUSIC] But it is not the end of the story. Our book has another part dealing with quantized light, indeed. There are phenomena that cannot be understood in the framework of the semi-classical model. Spontaneous emission, that is to say the fact that an isolated atom in an excited state eventually emits a photon, cannot be described consistently in the semi-classical model of matter light interaction. To describe correctly the phenomenon of spontaneous emission one needs to quantize light. Moreover, starting in the 1970s experimentalists could produce new states of radiation giving rise to phenomena that could not, absolutely not, be described by classical electromagnetism. For instance, it was possible to produce single photon wave packets or pairs of entangled photons exhibiting surprising behaviors impossible to describe by any classical model. Soon after in the mid-1980s, squeezed states of light were produced for the first time, allowing one to pass what had been considered a fundamental limit. The so-called standard quantum limit. Squeezed light can be used for measurements with an unprecedented sensitivity. For instance, in gravitational-waves detectors. This belongs to the domain of quantum metrology. Single and entangled photons are used to transmit and process information, in totally new ways, this is the domain of quantum information, a central theme in the second quantum revolution, which is underway. So to my first question, do we need to quantize light? The answer is yes, we need to quantize light if we want to understand modern optics. But why should you want to study quantization of light? I can offer at least three very good reasons. First, because you are interested in basic phenomena and you want to know how to describe correctly spontaneous emission. This was the only compelling reason when I was a student. Second, because you are interested in basic phenomena and you want to know how the new quantized states of light have allowed experimentalists to shed a new light on the conceptual foundations of quantum physics. I am one of these experimentalists and in this course, I will describe some experiments related to fundamental questions and share with you my amazement and enthusiasm about the way experiments allow us to address conceptual questions. Third, because you are convinced that quantum technologies will play an important role in the next decade, and you want to be able to understand key elements at the root of the second quantum revolution. With our younger colleagues Michel and I are involved in the second quantum revolution, and we will present some examples of quantum technologies. If you feel interested by at least one of these reasons, then come with us on our journey in quantum optics. [MUSIC] In fact, the matter is so broad, that we have decided to split our course in two parts. You are today embarking into our first course where you will learn how to quantize light, how to describe its evolution, its propagation in free space and in optical instruments, such as interferometers. Along the seven lessons of this first course, you will also learn many theoretical tools of quantum optics necessary to be able to read advanced books or research papers, and to do calculations yourself. But studying these theoretical tools without examples would be hard to swallow. Michel and I, we are experimentalists and we cannot conceive a course without real examples. In this first course, our privileged example of a fully quantum state of light will be one-photon wave packets. Before 1970, one could not even dream of producing such states even less to send them into an interferometer. Now days, it has become standard and such states are basic tools of quantum technologies. Let us now skim through the program of the seven lessons of our first course. In the lesson of today, you will learn how it is possible to quantize a classical electromagnetic field. We will consider the case of a single mode only in order to keep a simple enough formalism. The notion of photon will immediately emerge as well as a notion of vacuum fluctuations quite important in quantum optics. In lesson two, you will encounter a first model of one photon wave packet based on a single mode. After learning the expressions of single and double photo-detection signals, a basic tool in quantum optics, you will be able to appreciate the fully quantum property of one photon, its particle like behavior, and understand why the classical model of light cannot render an account of this behavior. In lesson three, we are going to address a question which has fascinated physicists since the early days of quantum physics. Can a single photon lead to interferences, that is to say a wavelike behavior. To describe the interferometer, you will need to learn how to describe the effect of a beam splitter on quantized light, another basic tool of quantum optics. In a real laboratory, one always deals with radiation that can be described only using several modes of the electromagnetic field. In the fourth lesson, you will learn about quantization of multimode radiation and about the generalization of the notion of photon and of photo detection signals. You will also find, why the question of vacuum fluctuations is far from trivial. In the fifth lesson, you will learn how to produce one-photon wave packets from the first sources of the early 1980s to the most recent ones. It will be also the right moment to learn another very important theoretical tool for quantum optics, the Heisenberg formalism. In lesson six, we will then be ready to describe real experiments which illustrate the concept of wave particle duality and of complementarity. I will argue that this is a real mystery, but a fruitful mystery, since it's only after they recognized this mysterious behaviour that creative physicists developed new quantum technologies central in the second quantum revolution. In lesson seven you will discover two quantum technologies based on one photon wave packets. Quantum random number generators and quantum cryptography. It will then be time to pause and digest all that matter before embarking in our second course which is in preparation. In each lesson you will have several quiz, usually quite simple. Useful to help you assimilate the main notions of the lesson. You will find such a quiz just at the end of this introduction as an example. Each lesson will be supplemented with a homework, which will not only help you to assimilate the subject of the lesson, but also to discover some additional phenomena or formalisms, which we consider important in modern quantum optics. So now it is time to start with us in the first leg of our journey and learn how to quantize light.
