Spin decoupling and line narrowing are observed for the first time in an optical transition, $^{3}H_{4}\ensuremath{\leftrightarrow}^{1}D_{2}$ of
Pr3+ in La
F3 at 2\ifmmode^\circ\else\textdegree\fi{}K, with use of optical free-induction decay. The
19F nuclei, when irradiated by an appropriate rf field, undergo forced precession about an effective field at the magic angle in the rotating frame. The fluctuating
19F-
19F dipolar interaction is thereby quenched and the optical linewidth drops from \ensuremath{\sim}10 to \ensuremath{\sim}2 kHz, as predicted in a theory of spin diffusion.
We report on the observation of a new magic frequency within the hyperfine structure of the D2 line of
87Rb atoms at which the scattering of light into a high-finesse cavity is suppressed by an interplay between quantum interference and the strong collective coupling of atoms to the cavity. Scattering from a cloud of laser-driven cold atoms into the cavity was measured in a polarization sensitive way. We have found that both the Rayleigh and Raman scattering processes into the near-resonant cavity modes are extinguished at 185 MHz below the F=2
↔F'=3 transition frequency. This coincidence together with the shape of the observed spectral dip imply that the effect relies on a quantum interference in the polariton excitations of the strongly coupled combined atom-photon system. We have also demonstrated the existence of a magic frequency around -506 MHz, where only the Raman scattering is suppressed due to a quantum interference effect at the single-atom level.