Single-photon nonlinear optics with Kerr-type nanostructured materials

We employ a quantum theory of the nonlinear optical response from an actual solid-state material possessing an intrinsic bulk contribution to the third-order nonlinear susceptibility (Kerr-type nonlinearity), which can be arbitrarily nanostructured to achieve diffraction-limited electro-magnetic-field confinement. By calculating the zero-time-delay second-order correlation of the cavity field, we set the conditions for using semiconductor or insulating materials with near-infrared energy gaps as an efficient means to obtain single-photon nonlinear behavior in prospective solid-state integrated devices, alternative to ideal sources of quantum radiation such as, e. g., single two-level emitters.