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arXiv · 1604.03914

Two photons co- and counter-propagating through $N$ cross-Kerr sites

Daniel J. Brod·Joshua Combes·Julio Gea-Banacloche
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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.

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Daniel J. Brod, Joshua Combes, Julio Gea-Banacloche. 2016-08-19. Two photons co- and counter-propagating through $N$ cross-Kerr sites. https://doi.org/10.1103/physreva.94.023833

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