Single-photon frequency conversion in nonlinear crystals

Frequency conversion of single photons in a nonlinear crystal is theoretically discussed. Losses and noise are included within a Heisenberg-Langevin formalism for the propagating photon field. We calculate the first- and second-order correlation functions of the frequency-converted light when the input is a train of single-photon pulses. This model allows one to identify the requirements on the nonlinear device so that it can be integrated in a quantum network.