Single-photon nonlinear optics with Kerr-type nanostructured materials

In this work, it is described 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). This material is assumed to be arbitrarily nanostructured to achieve diffraction-limited electromagnetic field confinement. By calculating the zero-time delay second-order correlation of the cavity field, the conditions are identified for using semiconductor or insulating materials with near-infrared energy gaps as 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. Thus, future quantum photonics applications can strongly benefit from the capability of nanostructuring ordinary Kerr-type materials to achieve sub-diffraction limited electromagnetic field confinement. The growing interest in integrated quantum photonics, and the possibility of fully exploiting the mature CMOS-based technology to build room-temperature and intrinsically flexible single-photon devices are likely to produce new research avenues based on the present proposal in the near future.