  We study the non-linear response of a 2+1 dimensional holographic model with
weak momentum relaxation and finite charge density to an oscillatory electric
field pump pulse. Following the time evolution of one point functions after the
pumping has ended, we find that deviations from thermality are well captured
within the linear response theory. For electric pulses with a negligible zero
frequency component the response approaches the instantaneously thermalizing
form typical of holographic Vaidya models. We link this to the suppression of
the amplitude of the quasinormal mode that governs the approach to equilibrium.
In the large frequency limit, we are also able to show analytically that the
holographic geometry takes the Vaidya form. A simple toy model captures these
features of our holographic setup. Computing the out-of-equilibrium probe
optical conductivity after the pump pulse, we similarly find that for
high-frequency pulses the optical conductivity reaches its final equilibrium
value effectively instantaneously. Pulses with significant DC components show
exponential relaxation governed by twice the frequency of the vector
quasinormal mode that governs the approach to equilibrium for the background
solution. We explain this numerical factor in terms of a simple symmetry
argument.
