Diffraction without a grating?

Can a matter wave be diffracted by two-counter propagating laser beams when their frequencies are different? Because two such laser beams create a beat pattern and not a standing wave, such a beat pattern might not be expected to give rise to a time-averaged potential from which the matter wave could diffract. However, in terms of photon scattering, energy and momentum can be conserved in this situation and diffraction would be expected. We resolved this paradox and theoretically predict that a time averaged potential is to be expected and diffraction should occur. The basic idea is that the incoming wave participates in forming the grating and subsequently diffracts from that grating. In other words, the grating does not exist separately from the wave. This process involves three photons, is non-linear in the laser intensity and has appropriate symmetry behavior. Supported by NSF and DOD-EPSCoR.