%0 Journal Article %T Magic frequencies in atom-light interaction for precision probing of the density matrix %A Menachem Givon %A Yair Margalit %A Amir Waxman %A Tal David %A David Groswasser %A Yonathan Japha %A Ron Folman %J Physics %D 2013 %I arXiv %R 10.1103/PhysRevLett.111.053004 %X We analyze theoretically and experimentally the existence of a {\it magic frequency} for which the absorption of a linearly polarized light beam by vapor alkali atoms is independent of the population distribution among the Zeeman sub-levels and the angle between the beam and a magnetic field. The phenomenon originates from a peculiar cancelation 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. %U http://arxiv.org/abs/1306.1151v1