Lévy Statistics and Laser Cooling

François Bardou obtained his Ph.D. in 1995 at the Ecole Normale Supérieure de Paris for his experimental and theoretical studies of laser cooling below the one photon recoil, and was the 1995 winner of the Aimé Cotton prize (Atomic Physics prize of the French Physical Society). He now works at the Centre National de la Recherche Scientifique (CNRS) where he works on stochastic problems in quantum tunnelling. Jean-Philippe Bouchard is a Senior Expert at the Service de Physique de l'Etat Condense and at CEA-Saclay. In 1994 he founded his own company called Science and Finance, and continues to have diverse research interests which include statistical physics, granular matter and theoretical finance. He is in charge of various statistical physics and finance courses in the Grandes Ecoles, Paris, and is the co-author of Theory of Financial Risk (Cambridge University Press, 2000). Alain Aspect is a Director of Research at CNRS and a Professor at the Ecole Polytechnique, Palaiseau. After completing a series of experiments in the early 1980s on the foundations of quantum mechanics, he joined Claude Cohen-Tannoudji at the Ecole Normale Supérieure to work on laser cooling of atoms. He is now head of the Atom Optics group of Institut d'Optique at Orsay and is the co-author of Introduction to Quantum Optics (Cambridge University Press, 2010). Claude Cohen-Tannoudji is Professor of Atomic and Molecular Physics at the Collège de France in Paris and was honoured with the Nobel Prize for Physics in 1997 for his work on the development of methods to cool and trap atoms with laser light. He is also the co-author of three other books: Quantum Mechanics (1992), Photons and Atoms: Introduction to Quantum Electrodynamics (1989), and Atom-Photon Interactions: Basic Processes and Applications (1998).

1. Introduction; 2. Subrecoil laser cooling and anomalous random walks; 3. Trapping and recyling. Statistical properties; 4. Broad distributions and Lévy statistics: a brief overview; 5. Proportion of atoms trapped in quasi-dark states; 6. Momentum distribution; 7. Physical discussion; 8. Tests of the statistical approach; 9. Example of application: optimization of the peak of cooled atoms; 10. Conclusion; Appendix A. Correspondence of the parameters of the statistical models with atomic and laser parameters; Appendix B. The Doppler case; Appendix C. The special case mu = 1.