Localization transition for light scattering by cold atoms in an external magnetic field

We establish a localization phase diagram for light in a random three-dimensional (3D) ensemble of motionless two-level atoms with a three-fold degenerate upper level, in a strong static magnetic field. Localized modes appear in a narrow spectral band when the number density of atoms $\rho$ exceeds a critical value ${\rho }_c\simeq 0.1k_0^3$, where $k_0$ is the wave number of light in the free space. A critical exponent of the localization transition taking place upon varying the frequency of light at a constant $\rho

\rho_c$isestimatedtobe$\nu = 1.57 \pm 0.07$. This classifies the transition as an Anderson localization transition of 3D orthogonal universality class.