Levy Dynamics of Single Laser-Cooled Atoms

Swati Singh, Yiwen Chu, Mikhail D. Lukin +1 more

François Bardou, Jean‐Philippe Bouchaud, Alain Aspect +1 more

Laser cooling of atoms provides an ideal case study for the application of Lévy statistics in a privileged situation where the statistical model can be derived from first principles. This book demonstrates how the most efficient laser cooling techniques can be simply and quantitatively understood in terms of non-ergodic random processes dominated by a few rare events. Lévy statistics are now recognised as the proper tool for analysing many different problems for which standard Gaussian statistics are inadequate. Laser cooling provides a simple example of how Lévy statistics can yield analytic predictions that can be compared to other theoretical approaches and experimental results. The authors of this book are world leaders in the fields of laser cooling and light-atom interactions, and are renowned for their clear presentation. This book will therefore hold much interest for graduate students and researchers in the fields of atomic physics, quantum optics, and statistical physics.

Jean Claude Garreau

Claude N. Cohen-Tannoudji

Laser Cooling now allows one to cool atoms below the single photon recoil limit. It will be shown that subrecoil cooling involves anomalous random walks in velocity space and that new physical insight can be obtained into this problem by using Lévy statistics. New possible applications of such ultracold atoms will be reviewed.

Uday Kumar Khan

Claude N. Cohen-Tannoudji

Atoms can now be laser cooled, in one, two and three dimensions, below the limit corresponding to the recoil energy of an atom absorbing or emitting a single photon. Recent works have shown that all subrecoil cooling schemes are based on an anomalous random walk of the atom in momentum space which does not obey the central limit theorem and which introduces a fundamental non–ergodicity in the cooling process. Lévy statistics turn out to be very useful for analysing such a situation since they provide quantitative results for the long time limit of the momentum distribution. In this paper, we briefly review these theoretical works and we give a few references where more details can be found. We also mention a few recent experiments which have been stimulated by these theoretical developments.