Ab InitioFew-Mode Theory for Quantum Potential Scattering Problems

Abstract

Few-mode models have been a cornerstone of the theoretical work in quantum optics, with the famous single-mode Jaynes-Cummings model being only the most prominent example. In this work, we develop ab initio few-mode theory, a framework connecting few-mode system-bath models to ab initio theory. We first present a method to derive exact few-mode Hamiltonians for non-interacting quantum potential scattering problems and demonstrate how to rigorously reconstruct the scattering matrix from such few-mode Hamiltonians. We show that upon inclusion of a background scattering contribution, an ab initio version of the well known input-output formalism is equivalent to standard scattering theory. On the basis of these exact results for non-interacting systems, we construct an effective few-mode expansion scheme for interacting theories, which allows to extract the relevant degrees of freedom from a continuum in an open quantum system. As a whole, our results demonstrate that few-mode as well as input-output models can be extended to a general class of problems, and open up the associated toolbox to be applied to various platforms and extreme regimes. We outline differences of the ab initio results to standard model assumptions, which may lead to qualitatively different effects in certain regimes. The formalism is exemplified in various simple physical scenarios. In the process we provide proof-of-concept of the method, demonstrate important properties of the expansion scheme, and exemplify new features in extreme regimes. *

Ab initio quantum models for thin-film x-ray cavity QED

“…Our first approach constitutes an ab initio version of the phenomenological few-mode model [45,46], based on our recent general framework for few-mode approaches to quantum scattering problems [71]. It removes the need for heuristic extensions and to fit the quantum optical parameters.…”

“…Overview of theoretical approaches to thin-film x-ray cavity QED with Mössbauer nuclei, including the standard semiclassical layer formalism [11], which is based on a variant of linear dispersion theory [63,64,67], and a successful phenomenological few-mode model [45,46], which is based on the quantum input-output formalism of cavity QED [70]. In this paper we present two additional ab initio quantum approaches to the problem, including an application of the ab initio few-mode theory [71] and of established Green's function techniques [72][73][74][75] to the layer geometry and the nuclear quantum optics setting. Besides completing the connections between the theories illustrated in this diagram and showing which approximations are involved in each case, the main results presented in this paper are indicated by the labeled magenta arrows.…”

Macroscopic QED for quantum nanophotonics: emitter-centered modes as a minimal basis for multiemitter problems

“…Given all the points above, it is not surprising that there are many different approaches to quantizing EM modes in lossy material systems [2,[7][8][9][10][11][12][13][14][15]. In the following, we give a concise overview of a particularly powerful formal approach that resolves these problems, called macroscopic QED [16][17][18][19][20][21][22][23][24].…”

“…It should be noted that in principle, both macroscopic QED and input-output theory can provide for a complete description of the system. In fact, a few-mode description suitable for treatment within input-output theory or master equation formalisms can be obtained from macroscopic QED by, essentially, "reversing" Fano diagonalization and reexpressing the EM modes through a finite number of discrete modes coupled to exterior continua[15,47].…”

Green's-function formalism for resonant interaction of x rays with nuclei in structured media

“…[37]. A recently developed general ab initio few-mode model for quantum potential scattering problems promises to be applicable also to x-ray thin-film cavities [38]. We note that after the submission of this work, another ab initio approach using Green's functions for nuclear quantum optics in x-ray cavities was brought to our attention [39].…”