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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.
Syllabus
- Week 1 - 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 ... - Week 2 - One photon state in a single mode: particle-like behaviour
In this lesson, you will discover how the quantum optics formalism leads to the particle-like behaviour of a one photon wave-packet. For this, you will have to learn the quantum optics expressions of the simple and joint photodetection signals. A comparison wi... - Week 3 - One photon interference: Wave-Particle duality
In this lesson, you will address the fascinating question of a single photon interfering with itself, by calculating the interference pattern for a single photon launched into a Mach-Zehnder interferometer. In order to do it you will first learn how to treat a... - Week 4 - Multimode quantized radiation: quantum optics in a real lab
In the real world there is nothing like purely monochromatic radiation. A correct description of radiation necessarily involves several modes. In this lesson, you will learn how canonical quantization can be easily generalized to the case of several modes, and... - Week 5 - One photon sources in the real world
One photon sources are important components in quantum optics, both in research laboratories and in applied quantum technologies. The lesson of this week will present the various kinds of one-photon sources available today, from heralded one photon sources to ... - Week 6 - Wave-particle duality for a single photon in the real world
You are now ready to develop the description of a real experiment , which was the first one to reveal directly the dual nature -- wave and particle, of a real single photon wave-packet. You will not only be able to describe, with the formalism you have learned... - Week 7 - One-photon based quantum technologies
In this lesson, you will discover two quantum technologies based on one photon sources. Quantum technologies allow one to achieve a goal in a way qualitatively different from a classical technology aiming at the same goal. For instance, quantum cryptography is...
Instructors
Alain Aspect
Professor
Physics
Michel Brune
Professor
Physics
Content Designer
École polytechnique (also known by the nickname " X ") is a French public institution of higher education and research, located in Palaiseau near Paris. It is one of the French Grandes écoles, and is renowned for its four-year undergraduate Ingénieur Polytechnicien degree in science and engineering. Students are usually admitted after two years of selective university-level preparation in mathematics and physics or after a Bachelor of Sciences (Licence in French educative system).
Polytechnique was established in 1794 by the mathematician Gaspard Monge during the French Revolution, and became a military academy under Napoleon I in 1804. Today, the institution still runs under the supervision of the French ministry of Defence. Initially located in the Latin Quarter of central Paris, the establishment was moved in 1976 to Palaiseau on the Saclay Plateau, southwest of Paris.
Polytechnique is a founding member of ParisTech, a grouping of leading Paris-area engineering colleges established in 2007. In 2014 it became a founding member as well as the head of multidisciplinary technology and innovation institute, the confederal "University of Paris in Saclay". Among its alumni are three Nobel prize winners, one Fields Medalist, three Presidents of France and many CEOs of French and international companies.
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