Fifteen years of cold matter on the atom chip: promise, realizations, and prospects.

Here we review the field of atom chips in the context of Bose-Einstein Condensates (BEC) as well as cold matter in general. Twenty years after the first realization of the BEC and 15 years after the realization of the atom chip, the latter has been found to enable extraordinary feats: from producing BECs at a rate of several per second, through the realization of matter-wave interferometry, and all the way to novel probing of surfaces and new forces. In addition, technological applications are also being intensively pursued.

Magic frequencies in atom-light interaction for precision probing of the density matrix.

We analyze theoretically and experimentally the existence of a magic frequency for which the absorption of a linearly polarized light beam by a vapor of alkali-metal atoms is independent of the population distribution among the Zeeman sublevels and the angle between the beam and a magnetic field. The phenomenon originates from a peculiar cancellation of the contributions of higher moments of the atomic density matrix, and is described using the Wigner-Eckart theorem and inherent properties of Clebsch-Gordan coefficients. One important application is the robust measurement of the hyperfine population.