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

Abstract

The resonant interaction between x-ray photons and nuclei is one of the most exciting subjects in the burgeoning field of x-ray quantum optics. A resourceful platform used to date is thin-film x-ray cavities with embedded layers or Mössbauer nuclei such as 57 Fe. A quantum optical model based on the classical electromagnetic Green's function is developed to investigate theoretically the nuclear response inside the x-ray cavity. The model is versatile and provides an intuitive picture about the influence of the cavity structure on the resulting spectra. We test its predictive powers with the help of the semiclassical coherent scattering formalism simulations and discuss our results on increasing complexity of layer structures.

Superradiance and anomalous hyperfine splitting in inhomogeneous ensembles

“…Refs. [46,50] provide a connection between the linear response of the quantum optical model [45,57] to the scattering model of Hannon, Trammel, Sturhahn et al Our work extends this quantum optical Green's function approach to include inhomogeneous hyperfine parameters, and provides an insight into how the inhomogeneity will enter into the non-linear dynamics of the system. In the following we provide a few illustrative examples.…”

“…A more recent model, developed by Heeg and Evers [45,57] has focused on the quantum optical perspective, with the emphasis being on the resonant interaction of the nuclei with the cavity mode. A Green's function approach for the scattering part of the Hamiltonian has been developed by Lentrodt et al [46] and Kong et al [50]. These works use analytic expressions for the Green's functions in layered media, developed by Tomaš [69] (and later on also by Johansson [70]), which can be expressed in terms of the layer matrix formalism for planar scattering.…”

“…Thus, the collective interaction can still play a significant role, however the interplay between the spectral inhomogeneity and the collective scattering results in non-trivial structure of the arXiv:2102.11183v1 [quant-ph] 22 Feb 2021 resulting spectra. To describe the dipole-dipole interaction we use a Green's function method, developed by Grüner and Welsch [47], which has been successfully applied to describe superradiance in diverse systems such as atomic clouds [10,11,48,49], one-dimensional waveguides [39,40], and thin film x-ray reflection [46,50]. A compact formula is found for the weak-excitation regime susceptibility, in terms of the coherent average of the emitters responses, with the collective interaction describable via a single complex constant.…”

Certifying multi-mode light-matter interaction in lossy resonators

“…Multi-mode level shift design.-Finally, we explore the multi-mode effects outlined above in the concrete platform of thin-film X-ray cavity QED with Mössbauer nuclei, which has recently attracted considerable theoretical [24,31,33,34,43,44] and experimental [25][26][27][28][29][30]45] attention, and similar setups with electronic processes are starting to be explored [46][47][48]. In these cavities, the atom is replaced by a thin layer containing an ensemble of Mössbauer nuclei.…”

“…As a result, single-mode models fail to quantitatively describe the nuclear spectra [24]. A key application of such cavitynuclei systems is to engineer artificial few-level quantum systems, which are otherwise inaccessible at hard X-ray energies [25][26][27][28][29][30][31][32][33][34]. In this case, the properties of the artificial quantum system crucially depend on multi-mode effects, in a way that is still poorly understood.…”