Nonclassical character of statistical mixtures of the single-photon and vacuum optical states

We demonstrate, theoretically and experimentally, that statistical mixtures of the vacuum state $|0〉$ and the single-photon Fock state $|1〉$ are nonclassical according to the Vogel criterion [W. Vogel, Phys. Rev. Lett. 84, 1849 (2000)], regardless of the vacuum fraction. The ensembles are synthesized via conditional measurements on biphotons generated by means of parametric down conversion, and their quadrature statistics are measured using balanced homodyne detection. A comparative review of various quantum state nonclassicality criteria is presented.