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.

Directivity of Radiating Quantum Source Systems

“…where D ij is now a constant device (sensitivity) tensor. 3 We may also expand the hermitian tensor D ij as a Hermitian matrix in the form…”

Numerical framework for modeling quantum electromagnetic systems involving finite-sized lossy dielectric objects in free space

“…(1) i (r) denotes the Whitney 1-form for i-th edge. Substituting (27) into (11) and performing the Galerkin testing, one can find the following linear system which is the discrete counterpart of (11) expressed by…”

“…It implies that when analyzing interactions between atoms and EM fields around plasmonic nano-particles or structures, one has to consider effects of BA fields as well as MA fields. Note that there are several previous works that appreciated and recognized the importance of BA effects in analyzing, for example, input-output relations for a lossy beam splitter [25], an optical cavity made of lossy dielectric slabs [26], and quantum antennas and scattering of nonclassical lights based on super-operator equations [27].…”