Atoms and Photons
- This lecture aims at the description of the interaction between quantum matter in its simplest form, an atom, and an electromagnetic field. A semi-classical approach, where the field is classical, is first considered, including relaxation of the atom. We then study the quantization of the electromagnetic field and its relaxation, before its interaction with an atom is described in a full quantum model.
Lectures notes in English written by Jean-Michel Raimond available here with handout slides, and edited by Hélène Perrin there.
The concepts studied during the lecture are illustrated in the tutorials by applications in experimental physics, making the connection to current research activities (cold atoms, quantum optics, cavity QED).
- Classical and phenomenological approaches to light-matter coupling. Harmonically bound electron, Einstein’s coefficients.
- Semi-classical approach. Atom-field interaction Hamiltonian. Perturbative solution for the non-resonant interaction. Resonant interaction : Rabi oscillation and applications, Ramsey interferometry. Atomic relaxation : Kraus processes, Lindblad equations and quantum jumps. Optical Bloch equations and applications : saturation, saturation spectroscopy, EIT, Maxwell-Bloch equations, slow light.
- Field quantization. Eigenmodes of the classical field, normal variables, field energy, momentum and angular momentum. Field Hamiltonian, creation and annihilation operators, field operators. Quantum states of the field : Fock states, coherent states. Phase space representations, Wigner function. Coupling of field modes : beam-splitter model. Field relaxation : Lindblad equation and evolution of states.
- Quantum field coupled with quantum matter. Atom-field interaction. Spontaneous emission. Photo-detection signals and intensity correlations, Hanbury-Brown and Twiss, bunching and anti-bunching. Jaynes and Cummings model, cavity quantum electrodynamics. Applications : from Purcell effect to strong coupling. Collective emission, super-radiance.
Bibiliography
- C. Cohen-Tannoudji, J. Dupont-Roc and G. Grynberg, “An introduction to quantum electrodynamics” and “Photons and atoms”, Wiley, 1992
- S. Haroche and J.-M. Raimond “Exploring the quantum”, OUP 2006
- G. Grynberg, A. Aspect and C. Fabre, “Introduction to Quantum Optics”, Cambridge University Press (2010)
- C. Cohen-Tannoudji and D. Guéry-Odelin “Advances in atomic physics : an overview”, World Scientific 2012
The course assumes an excellent command of basic quantum physics: Dirac formalism, operators, measurement, Hamiltonian dynamics, spin-1/2, elementary atomic physics (hydrogen), harmonic oscillator (basically all of Volume 1 of the Cohen-Tannoudji, Diu and Laloë classic textbook).
A working knowledge of density operator is also required, as well as a good knowledge of classical electromagnetism: Maxwell equations, propagation equations, limiting conditions, plane waves, spherical waves, dipole radiation (see the Jackson for instance).
Homework and written exam
