Single-photon scattering by two separated atoms in a supercavity

We study the single-photon scattering along a one-dimensional cavity array with two distant two-level atoms in a supercavity, which aims to simulate a recent x-ray experiment Nature 482, 199 (2012). Without introducing dissipation, we find that when one atom is exactly located at a node of a mode of the supercavity and the other is at the antinode of that mode, no splitting of the reflectivity peak can appear. Nevertheless, the atom at the node significantly changes the positions of the reflectivity valleys. On the other hand, when the atom is shifted a little from the exact node, then the splitting can appear. We also explain these results with an analysis based on the general formal scattering theory. Our result implies the importance of non-resonant modes of the supercavity in our problem.