Production of heralded pure single photons from imperfect sources using cross phase modulation

Realistic single-photon sources do not generate single photons with certainty. Instead they produce statistical mixtures of photons in Fock states $\ket{1}$ and vacuum (noise). We describe how to eliminate the noise in the output of the sources by means of another noisy source or a coherent state and cross phase modulation (XPM). We present a scheme which announces the production of pure single photons and thus eliminates the vacuum contribution. This is done by verifying a XPM related phase shift with a Mach-Zehnder interferometer.