Elective courses, M2 First semester, courses
Quantum theory of electromagnetism
- Classical electromagnetism before quantum electrodynamics: Maxwell’s equations in Fourier space, transverse and longitudinal modes, energy and momentum, gauges choices: Coulomb and radiation.
- Schrödinger’s equation in the presence of a classical electromagnetic field, perturbation theory and Fermi’s Golden Rule, excitation rates.
- The Fock space of the quantum electromagnetic field, photons, the interaction Hamiltonian between matter and the electromagnetic field.
- Some properties of the quantum electromagnetic field: energy, momentum and angular momentum; vacuum fluctuations and the Casimir effect.
- Some remarkable states of the quantum electromagnetic field: coherent states and squeezed states, classical limit of quantum electromagnetism.
- The interaction between photons and matter: absorption and emission of a single photon by an atom, spontaneous emission, laser, the Weisskopf-Wigner model.
- If time allows: entangled photons and the violation of Bell’s inequalities.
Production of two electron-positron pairs. In this photo from the 15-foot bubble chamber at Fermilab, USA, gamma-ray photons turn into electron-positron pairs, matter & antimatter.
Quantum electromagnetism, photons, interaction between matter and light, spontaneous emission, classical and quantum states of light.
- Rayonnement quantique, Alain Laverne, available in French on: https://cel.archives-ouvertes.fr/cel-00092934
- Photons – Optique quantique, Majeure de Physique de l’Ecole Polytechnique, A. Aspect, P. Grangier, G. Grynberg (in French)
- Introduction to Quantum Optics, G. Grynberg, A. Aspect, C. Fabre, Cambridge University Press
- Free online lectures by A. Aspect (in english): https://www.polytechnique.edu/elearning/fr/alain-aspect
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