  We present equilibrium and out-of-equilibrium studies of the Verwey
transition in magnetite. In the equilibrium optical conductivity, we find a
step-like change at the phase transition for photon energies below about 2 eV.
The possibility of triggering a non-equilibrium transient metallic state in
insulating magnetite by photo excitation was recently demonstrated by an x-ray
study. Here we report a full characterization of the optical properties in the
visible frequency range across the non-equilibrium phase transition. Our
analysis of the spectral features is based on a detailed description of the
equilibrium properties. The out-of-equilibrium optical data bear the initial
electronic response associated to localized photo-excitation, the occurrence of
phase separation, and the transition to a transient metallic phase for
excitation density larger than a critical value. This allows us to identify the
electronic nature of the transient state, to unveil the phase transition
dynamics, and to study the consequences of phase separation on the
reflectivity, suggesting a spectroscopic feature that may be generally linked
to out-of-equilibrium phase separation.
