We theoretically analyze the electron dynamics in a superlattice (SL) driven by a highly asymmetric electromagnetic pulse. We show that the time asymmetry of the pulse results in indirect population of higher minibands and leads to the appearance of a direct current. At low temperatures and low filling of the lowest miniband the current generated in the SL has an oscillating behavior as a function of the pulse strength with minima occurring when the wave vector transferred by the pulse matches an integer of half the reciprocal lattice constant. (c) 2006 Elsevier B.V. All rights reserved.