  We study prethermalization phenomena in weakly interacting Hubbard systems
after electric-field pump pulses with finite duration. We treat the Hubbard
interaction up to second order, applying the prethermalization paradigm for
time-dependent interaction protocols, and the electric field strength beyond
linear order. A scaling behavior with pulse duration is observed for the
absorbed energy as well as individual prethermalized momentum occupation
numbers, which we attribute to the leading quadratic orders in interaction and
electric field. We show that a pronounced non-thermal momentum distribution can
be created with pump pulses of suitable resonance frequencies, and discuss how
to distinguish them from thermal states.
