A heralded single-photon source implemented with second-order nonlinear photonic crystals

We study implementing a heralded single-photon source with second-order nonlinear photonic crystals. Injecting pump and signal light beams into a one-dimensional photonic crystal composed of a material with a large second-order nonlinear optical susceptibility $\chi^{(2)}$, we can transform the coherent incident signal light into squeezed light. Preparing two squeezed light beams by this method and input them into two ports of a 50-50 beam splitter independently, we can transform them into a two-mode squeezed state. Because those two modes of photons share entanglement, a single photon of the one mode is emitted with a high probability on the condition of the single-photon detection of the other mode as a heralding signal. We evaluate the efficiency and the second-order intensity correlation function $g^{(2)}(0)$ for this heralded single-photon source. Moreover, we examine changes in the efficiency and $g^{(2)}(0)$ when we assume that the single-photon detector for the heralding signal is imperfect. For a specific concrete example, we consider a case where the nonlinear medium is lithium niobate $\mbox{LiNbO}_{3}$ and the frequency of the incident signal light is on the order of $10^{14}$ Hz.