We have studied the transport properties of electrons in asymmetric quantum well structures upon far-infrared optical excitation of carriers from the lowest subband into the continuum. Here the photocurrent consists of a coherent component originating from ballistic transport upon excitation, and of an incoherent part associated with asymmetric diffusion and relaxation processes, which occur after the coherence has been lost. The signature of the coherent contribution is provided by a sign reversal of the photocurrent upon changing the excitation energy. This sign reversal arises from the energy-dependent interference between continuum states, which have a twofold degeneracy characterized by positive and negative momenta. The interference effect also allows us to estimate the coherent mean free path (>20nm at 77K). In specifically designed device structures, we use both the coherent and incoherent components in order to achieve a pronounced photovoltaic infrared response for detector applications.