A “Magic Frequency” for Atomic Spectroscopy
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