Controlling nonlinear photon-photon interaction via a two-level system. (arXiv:1801.03675v1 [quant-ph])

The problem of photon-photon interaction controlled by a two-level system is
studied in this paper. Specifically, we have proposed two scenarios: Case 1,
how a two-level system changes the pulse shapes of two initially uncorrelated
input photons in a single input channel; and Case 2, how a two-level system
entangles two counter-propagating photons, one in each input channel. The
steady-state output field states for both cases are derived explicitly. For
Case 1, the Wigner spectrum is used to exhibit the interesting properties of
the output field state. For Case 2, the nonlinear property of the interaction
between the two-level system and the two input photons has been revealed by the
probabilities of observing photons in the output channels. In addition,
two-photon interference, similar to Hong-Ou-Mandel effect, occurs when the two
input photons are chosen with the same pulse shape.

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