Quantum Modeling of Scanning Near-Field Optical photons Scattered by an Atomic-Force Microscope Tip for Quantum Metrology

Scattering scanning near-field optical microscopy (s-SNOM) is a promising technique for overcoming Abbe diffraction limit and substantially enhancing the spatial resolution in spectroscopic imaging. The s-SNOM works by exposing an atomic force microscope (AFM) tip to an optical electromagnetic (EM) field, while the tip is so close to a dielectric sample that the incident beam lies within the near-field regime and displays nonlinear behaviour. We replace the incident EM field by photons generated by a single photon emitter, and propose a quantum model for the suggested system by employing electric-dipole approximation, image theory, and perturbation theory. Quantum state of scattered photons from the AFM tip is extracted from the proposed model, which contains information about electrical permittivity of the dielectric material beneath the tip. The permittivity of the sample can be extracted through spectroscopic setups. Our proposed scheme has potential applications for high-resolution quantum sensing and metrology, especially for quantum imaging and quantum spectroscopy.