The role of the mode function in complementarity: A double-slit experiment with entangled photons in different modes

We probe the principle of complementarity which is central to quantum mechanics by performing and analyzing a double-slit experiment based on entangled photons created by spontaneous parametric down-conversion due to a pump mode with a coherent double-hump structure (TEM01-mode). In particular, we emphasize the need for a careful selection of the signal-idler photon pairs involved in the corresponding study of visibility and distinguishability. Indeed, when the signal photons interfering at the double slit belong to this double-hump mode we obtain almost perfect visibility of the interference fringes and no which-slit information is available. However, when we break the symmetry between the two maxima of the mode by detecting the entangled idler photon, the paths through the slits become distinguishable and the visibility vanishes. The mode function selected by the detection system decides if interference or which-slit information is accessible in the experiment.