Two photons co- and counterpropagating through N cross-Kerr sites

@article{Brod2016TwoPC,
  title={Two photons co- and counterpropagating through N cross-Kerr sites},
  author={Daniel Jost Brod and Joshua Combes and Julio Gea-Banacloche},
  journal={Physical Review A},
  year={2016},
  volume={94},
  pages={023833}
}
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 $S$ matrices for fields propagating in a medium where the cross-Kerr interaction is spatially distributed at… 

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