Abstract
We develop two ab initio quantum approaches to thin-film x-ray cavity quantum electrodynamics with spectrally narrow x-ray resonances, such as those provided by M\"ossbauer nuclei. The first method is based on a few-mode description of the cavity, and promotes and extends existing phenomenological few-mode models to an ab initio theory. The second approach uses analytically-known Green's functions to model the system. The two approaches not only enable one to ab initio derive the effective few-level scheme representing the cavity and the nuclei in the low-excitation regime, but also provide a direct avenue for studies at higher excitation, involving non-linear or quantum phenomena. The ab initio character of our approaches further enables direct optimizations of the cavity structure and thus of the photonic environment of the nuclei, to tailor the effective quantum optical level scheme towards particular applications. To illustrate the power of the ab initio approaches, we extend the established quantum optical modeling to resonant cavity layers of arbitrary thickness, which is essential to achieve quantitative agreement for cavities used in recent experiments. Further, we consider multi-layer cavities featuring electromagnetically induced transparency, derive their quantum optical few-level systems ab initio, and identify the origin of discrepancies in the modeling found previously using phenomenological approaches as arising from cavity field gradients across the resonant layers.
Highlights
In recent years, quantum optics with x rays has become an active field of research [1,2,3,4,5,6], driven by the progress in high photon intensities and beam quality at modern light sources [6,7,8,9]
In the third mode, where the electromagnetically induced transparency (EIT) phenomenon is observed, a different functional dependence and a negative γ12 is found. These results show how complex cavity structures can be unambiguously interpreted in terms of quantum optical models, which paves the way for designing effective nuclearlevel schemes via tailored mode environments
We have presented two ab initio approaches to describe thin-film x-ray cavities doped with narrow resonances such as those provided by Mössbauer nuclei on a quantum mechanical level
Summary
Quantum optics with x rays has become an active field of research [1,2,3,4,5,6], driven by the progress in high photon intensities and beam quality at modern light sources [6,7,8,9]. The nuclear resonant scattering community has largely employed semiclassical or meanfield methods based on perturbative scattering theory for the various transitions [58,59,60,61,62], including variants of linear dispersion theory [63,64] known as the layer [11,65,66] or Parratt’s [67] formalism, Shvyd’ko’s time and space picture [68], and Maxwell-Bloch equation treatments [29,68] These approaches enable one to accurately model the related experiments, which so far essentially operate in the weak-excitation regime. The first few-mode theory rigorously justifies and extends the phenomenological models and completes connections between existing approaches, while the second approach based on Green’s functions provides a computationally highly efficient avenue to the nuclear scattering problem Both approaches are applicable at weak coupling, but offer different advantages in more extreme regimes, as we discuss in detail. Details on derivations and parts of the calculations, as well as an in-depth practical comparison of the phenomenological and ab initio few-mode model are provided in the appendices
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