Welcome to the last lesson of our introductory course on quantum optics. You may feel surprised that it is already finished, although you have not heard of squeezed states of light, quasi-classical states, matter light interaction, you name what you think is missing. I am sure you would like also to hear about entangled photons and Bell's inequality tests and their use in quantum technologies. I want to reassure you, all these quantum topics will be presented in our second course, which is in preparation. But you should not underestimate what you have already learned. Much was based on the example of one photon wave packets: You may think it is a too narrow subject. Actually the properties of one photon wave packets belong to the very core of quantum optics. By learning how to describe them and understanding their properties, you have learned many important concepts of quantum optics. As important, to describe these properties, you have learned a lot of quantum optics formalism. This can lead you quite far, and allow you to read many research articles on quantum optics. So we thought it would be a good point for a pause, before embarking into a new course. But before this break, you should be interested in some practical applications of one photon wave packets which are important examples of quantum technologies, a rapidly developing field. Let me set the stage for quantum technologies, starting with the first quantum revolution. You all know that quantum physics discovered and elaborated in the first decades of the 20th century, allowed physicists to understand the mechanical, electrical, optical properties of matter, and of radiation. This understanding led to the invention of technologies that have profoundly modified our society. The transistor, invented in 1947, and the integrated circuits, invented in 1958, have led to the development of computers with exponentially growing capacities. The laser, invented in 1960, and the optical fiber, invented a few years later, have led to unbelievably large rates of data transfer. The result is the information and communication society, a totally new world. One can safely claim that these quantum technologies have changed the society as much as the invention of the heat engine did it, two centuries ago. Note that these inventions were done by outstanding physicists, who had fully understood and contributed to clarify the basic quantum concepts. Now. According to many physicists, including me, we are living a second quantum revolution, which started in the last decade of the twentieth century. It is based on two ingredients. Firstly, an amazing quantum property, entanglement, discussed between Einstein and Bohr from 1935 until their death. In fact, entanglement started to draw the attention of physicists only after John Stuart Bell published his famous Inequalities in 1964. Entanglement will be studied in our second course. The other ingredient of the second quantum revolution is the possibility to observe, control, and give comprehensive theoretical description of individual quantum objects. More precisely, starting in the 1970s, physicists have developed methods to observe and control single electrons, ions, individual atoms, and single photons, as you have learned in this course. It is now possible to observe the behavior of each atom in an ensemble of thousands of them, to control each ion in a chain of more than ten of them, and to observe the life and death of a single photon. The second quantum revolution is not only conceptual: It aims at using these new ingredients to develop totally new technologies of which we could not even dream, before developing the new concepts. Only a few new technologies have been fully developed yet. We will see today two such quantum technologies based on our ability to produce and manipulate one-photon wave packets. One is Quantum Random Number Generation, and the other one is Quantum Cryptography. As in previous lessons, I will not miss the opportunity to teach you some important elements of quantum optics formalism. In section two, I will give some properties of a weak classical light pulse, so weak, that the average energy per pulse is less than the energy of one photon. In contrast with what you could think, such pulses are dramatically different from one photon wave packets. It is crucial to understand these differences to use them in quantum cryptography. A central notion in quantum information is the notion of qubits, or quantum bits. Qubits can be realized with many different kinds of supports: atoms, ions, superconducting devices, semiconductor devices, but I will introduce them using one photon polarization. It will demand you to learn how to describe polarization in quantum optics and how to measure it. This will complete your knowledge of one-photon wave packets. You will then be ready to fully understand quantum cryptography, whose security is fundamentally better than usual cryptography. I will explain you the BB84 scheme, which is based on one-photon wave packets and quantum random number generators. In order to fully appreciate why quantum cryptography is secure, you must know a fundamental theorem of quantum physics, the no-cloning theorem. I will teach you this somewhat recent theorem which is a cornerstone of many quantum technologies. It is fundamental to better appreciate some of the basic concepts of quantum physics. I will thus give you a full demonstration. At this point it will be time to conclude this lesson, and the whole course.
