Today, you have heard about the second quantum revolution. Based on concepts that have emerged in recent decades, the second quantum revolution has already led to applications without any equivalent in classical technologies. I have presented two quantum technologies based on the unique properties of one-photon wave-packets. Quantum random number generators are based on the fact that a single photon, impinging on a beam splitter, will be either transmitted or reflected, in a fundamentally random fashion, as far as we understand quantum mechanics. This is in contrast to standard classical random number generators, which are in fact pseudo random number generators of which sophisticated technology could in principle guess the outcome. You have then learned about quantum cryptography. It is based on a classical scheme. The one time pub cryptography scheme. What is quantum is the quantum key distribution scheme. A remarkable example is the BB84 QKD scheme, which is based on the fact that it is impossible to fully determine the quantum state of a single quantum object. More precisely the polarization of a single photon. The no-cloning theorem is crucial to demonstrate the security of the BB84 scheme. It is also at the root of other QKD schemes which we will encounter in our second course. One should not underestimate the importance of quantum cryptography which is fundamentally secure. It is a contrast with usual cryptography, whose security depends on the hypothesis that you advisory, the eaves dropper, has neither a technology nor a mathematical level much better than yours. To understand what I mean consider the standard cryptographic scheme used on internet, the RSA scheme. It relies on the fact that factoring large numbers takes a very long time, so its security depends on two hypothesis. First, that there is no mathematical method unknown to us for fast factorization. Second, that the adversary has not a computer much faster than ours. With the always increasing efficiency of computers, it is in fact likely that secret messages of today will become easily deciphered a decade from now. There are ultra sensitive messages, for instance, in the domain of diplomacy, which governments would not like to see publicized after ten years only. This is a good enough reason to consider cryptography. Indeed, as far as we know, quantum cryptography is immune to any technological or mathematical progress. Of course, if we discover a breach in quantum physics, this statement might turn out to be wrong. But the laws of quantum physics seem to be extremely solid. And have resisted all attacks for almost one century. As in previous lessons, you have also learned some basic technical tools of the quantum optics formalism. Today it was the description of photon polarization, a very important formalism that plays a role in many quantum optics phenomena. I've also alluded to some properties of weak classical light pulses, which should not be confused with one-photon wave packets, even when the average energy per classical pulse is less than the energy of a single photon. Surprising, isn't it? To fully appreciate this statement, you will have to join us again in our second course on quantum optics where you will learn the formalism of quasi-classical quantum states of light. This lesson Is the last one of our first course on quantum optics. In this course, you have learned many fundamental tools of the quantum optics formalism. How to describe quantum radiation, as a set of quantum harmonic oscillators. How to describe optical instruments and devices. In particular those including beam-splitters, using the Heisenberg formalism. How to calculate single and double photo-detection signals. You have discovered how to describe polarized single photon wave packets, which have properties absolutely impossible to describe and to understand in the framework of classical electromagnetism. All this constitutes a broad knowledge which should allow you to understand many phenomena of quantum optics, including some quantum technologies belonging to the second quantum revolution. You must be aware, however, that in order to cover the whole field of quantum optics, you need to learn a little more. This will be the aim of our second course on quantum optics. The planned menu of our second course, is as rich as the menu of a French restaurant. In addition, to the formalism of quasi-classical states of light crucial to understand where is the frontier between classical optics and quantum optics. there is another element central in quantum optics that I have deliberately ignored in this first course. The interaction between quantum radiation and quantized matter. More precisely atom, ion, molecule or solid. You will learn how to describe it. And it will when be possible to give a clear description of a phenomenon impossible to describe consistently in classical physics: Spontaneous emission, the fact that an atom in an excited state can spontaneously jump to a lower state and emit one photon. Then comes an extraordinary feature of quantum physics that I have named on several occasions, entanglement. That is to say, the fact that there are states of several photons in which the properties of the ensemble is much more than the ensemble of the properties of each individual photon. Entangled states offer fantastic possibilities to store and process information and are the heart of current research on quantum information. I hope that after digesting our first course, you will have appetite for these fascinating topics. If you liked this first course, see you next year, for more wonders in quantum optics. Bye bye.
