  We present a computational technique to calculate time and momentum resolved
non-equilibrium spectral density of correlated systems using a tunneling
approach akin scanning tunneling spectroscopy. The important difference is that
our probe is extended, basically a copy of the sample, allowing one to extract
the momentum information of the excitations. We illustrate the method by
measuring the spectrum of a Mott-insulating extended Hubbard chain after a
sudden quench with the aid of time-dependent density matrix renormalization
group (tDMRG) calculations. We demonstrate that the system realizes a
non-thermal state that is an admixture of spin and charge density wave states,
with corresponding signatures that are recognizable as in-gap sub-bands. In
particular, we identify a band of excitons and one of stable anti-bound states
at high energies that gains enhanced visibility after the pump. We do not
appreciate noticeable relaxation within the time-scales considered, which is
attributed to the lack of decay channels due to spin-charge separation. These
ideas can be readily applied to study transient dynamics and spectral
signatures of correlation-driven non-equilibrium processes.
