  We measure the absolute absorption cross section of molecules using a
matter-wave interferometer. A nanostructured density distribution is imprinted
onto a dilute molecular beam through quantum interference. As the beam crosses
the light field of a probe laser some molecules will absorb a single photon.
These absorption events impart a momentum recoil which shifts the position of
the molecule relative to the unperturbed beam. Averaging over the shifted and
unshifted components within the beam leads to a reduction of the fringe
visibility, enabling the absolute absorption cross section to be extracted with
high accuracy. This technique is independent of the molecular density, it is
minimally invasive and successfully eliminates all problems related to
photon-cycling, state-mixing, photo-bleaching, photo-induced heating,
fragmentation and ionization. It can therefore be extended to a wide variety of
neutral molecules, clusters and nanoparticles.
