Research on quantum statistic properties of photon number in pulse mode nonlinear frequency up-conversion

Frequency conversion technique attracts increasing attention in the applications in quantum optics. While the single-photon level pulse mode frequency conversion's quantum photon number statistics and quantum transmission theory still need to be improved. The photon number statistical distribution and quantum state transference in the interaction picture are discussed by three-wave mixing equation of the nonlinear frequency up-conversion, where the signal photons and pump light field are either continuous wave or Gaussian-shaped pulse mode. The results show that in different modes of signal photons and pump light field interaction, the photon number statistical distribution can be transferred and remain the same as the incident signal photon in the nonlinear frequency conversion process. These results have important reference value for the development of new quantum up-conversion devices and quantum control devices which are based on quantum frequency conversion.