Super-Operator Linear Equations and Their Applications to Quantum Antennas and Quantum Light Scattering

Abstract

In this paper, we develop a resolvent method for super-operator equations with applications in quantum optics. Our approach is based on the novel concept of a linear super-operator acting on the Hilbert subspace of vector or scalar linear operators satisfying physically reasonable commutation relations. The super-operator equations for the electromagnetic (EM) field operators are formulated for the problems of quantum antenna emission and quantum light scattering by a dielectric body. The general solution of super-operator equation is presented in terms of the classical resolvent. In contrast to the classical case, it includes the ancillary components associated with the quantum noise even in the absence of absorption. The reason for this lies in the energy exchange between different spatial regions with various bases for the field presentation (which looks like losses or gain from the point of view of the correspondent region). A number of examples (a two-element dipole antenna, a plane dielectric layer, and a dielectric cylinder with a circular cross section) which demonstrate the physical mechanism of the appearance of noise are considered. It is shown that antenna emission or scattering transforms the coherent properties of quantum light. This leads to a new way of controlling coherence in a direction-dependent manner, a feature that can be useful in various applications of quantum technologies, including quantum radars and lidars, and quantum antennas.