  Searching for Anderson localization of light in three dimensions has
challenged experimental and theoretical research for the last decades. Here the
problem is analyzed through large scale numerical simulations, using a
radiative Hamiltonian i.e. a non-Hermitian long-range hopping Hamiltonian, well
suited to model light-matter interaction in cold atomic clouds. Light
interaction in atomic clouds is considered in presence of positional and
diagonal disorder. Due to the interplay of disorder and cooperative effects
(sub- and super-radiance) a novel type of localization transition is shown to
emerge, differing in several aspects from standard localization transitions
which occur along the real energy axis. The localization transition discussed
here is characterized by a mobility edge along the imaginary energy axis of the
eigenvalues which is mostly independent from the real energy value of the
eigenmodes. Differently from usual mobility edges it separates extended states
from hybrid localized states and it manifest itself in the large moments of the
participation ratio of the eigenstates. Our prediction of a mobility edge in
the imaginary axis, i.e. depending on the eigenmode lifetime, paves the way to
achieve control both in the time and space domain of open quantum systems.
