Not yet reviewed by Pith; the record is open.

Single photons and single-photon pairs, inherently nonclassical in their nature, are fundamental elements of quantum sciences and technologies. Here, we propose to realize the nonclassical correlated deterministic photon pairs at the single-photon level for a single atom trapped in bimodal cavities. It is shown that the photon emissions for bimodal cavities exhibit a high single photon purity and relatively large intracavity photon numbers, which are ascribed to the combination of optical Stark shift enhanced energy-spectrum anharmonicity and quantum interference suppressed two-photon excitation. Our scheme generates photon-photon pairs with strong photon blockade for cavity modes via constructing a highly tunable cavity-enhanced deterministic parametric down-conversion process. Furthermore, we show that the cross-correlation function between the two cavity modes vastly violates the Cauchy-Schwarz inequality of the classical boundary, which unambiguously demonstrates the nonclassicality of the single-photon pairs. Our result reveals a prominent strategy to generate the high-quality two-mode single-photon sources with strong nonclassical correlation, which could provide versatile applications in distribution of quantum networks, long distance quantum communication, and fundamental tests of quantum physics.