Two photons co- and counter-propagating through cross-Kerr sites
arXiv:1604.03914 · doi:10.1103/PhysRevA.94.023833
Abstract
A cross-Kerr interaction produces a phase shift on two modes of light proportional to the number of photons in both modes, and is sometimes called cross-phase modulation. Cross-Kerr nonlinearities have many applications in classical and quantum nonlinear optics, including the possibility of a deterministic and all-optical controlled-phase gate. We calculate the one- and two-photon S-matrix for fields propagating in a medium where the cross-Kerr interaction is spatially distributed at discrete interaction sites comprised of atoms. For the interactions considered, we analyze the cases where the photons co-propagate and counter-propagate through the medium and give a physical interpretation to the differences between the two cases. Finally, we obtain the S-matrix in the limit of infinitely long chains, showing that it corresponds to a perfect controlled-phase operation.
15 pages (+ appendix), 7 figures. V2: New author added. Content expanded with new results (Sec. VIII). V3: Closer to published version. See companion paper at http://arxiv.org/abs/1604.04278
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