Limits on manipulating conditional photon statistics via interference of weak lasers.

Photon anti-bunching, measured via the Hanbury-Brown-Twiss experiment, is one of the key signatures of quantum light and is tied to sub-Poissonian photon number statistics. Recently, it has been reported that photon anti-bunching or conditional sub-Poissonian photon number statistics can be obtained via second-order interference of mutually incoherent weak lasers and heralding based on photon counting [Phys. Rev. A92, 033855 (2015)10.1103/PhysRevA.92.033855; Opt. Express24, 19574 (2016)10.1364/OE.24.019574; https://arxiv.org/abs/1601.08161]. Here, we report theoretical analysis on the limits of manipulating conditional photon statistics via interference of weak lasers. It is shown that conditional photon number statistics can become super-Poissonian in such a scheme. We, however, demonstrate explicitly that it cannot become sub-Poissonian, i.e., photon anti-bunching cannot be obtained in such a scheme. We point out that incorrect results can be obtained if one does not properly account for seemingly negligible higher-order photon number expansions of the coherent state.