QED theory for small-hole diffraction: Young diffraction from two Bethe holes

Abstract

Based on a recently developed quantum theory for a two-level quantum well screen with a mesoscopic hole [J. Jung and O. Keller, Phys. Rev. A 98, 053825 (2018)] a quantum electrodynamical (QED) theory for diffraction of light from mesoscopic holes is presented. A propagator formalism is used to calculate the super $\mathbf{S}$ matrix, relating the scattered field operators to the incident field operators in the Heisenberg picture. The developed QED formalism accounts for electric dipole (ED), magnetic dipole (MD), and electric quadrupole (EQ) diffraction and it opens up for the analysis of mesoscopic hole diffraction of, e.g., squeezed, entangled, and coherent quantum states of light. The theory is exemplified via a study of Young diffraction from two mesoscopic holes paying particular attention to MD and EQ scattering. The scattering of a single-photon state composed of just two plane-wave components both with wave vectors directed perpendicular to the screen is obtained. It is shown from a detailed calculation of the polarization selection rules that the relative importance of the MD and EQ scattering varies with the scattering angle. The single-photon counting signal is determined as a function of one of the two incoming frequencies, keeping the other fixed near the two-level quantum well (Bohr) resonance.