  Dipole-dipole interactions are at the origin of long-lived collective atomic
states, often called subradiant, which are explored for their potential use in
novel photonic devices or in quantum protocols. Here, we study subradiance
beyond linear optics and experimentally demonstrate a two hundred-fold increase
in the population of these modes, as the saturation parameter of the driving
field is increased. We attribute this enhancement to a mechanism similar to
optical pumping through the well-coupled superradiant states. The lifetimes are
unaffected by the pump strength, as the system is ultimately driven toward the
single-excitation sector.
