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arXiv:2205.06586 · Physical Review A

Inverse design in nuclear quantum optics: From artificial x-ray multilevel schemes to spectral observables

Oliver Diekmann, Dominik Lentrodt, Jörg Evers

Published Nov 1, 2022• 6 citations
arXivHTMLPDF

Abstract

Ensembles of M\"ossbauer nuclei embedded in thin-film cavities form a promising platform for x-ray quantum optics. A key feature is that the joint nuclei-cavity system can be considered as an artificial x-ray multilevel scheme in the low-excitation regime. Using the cavity environment, the structure and parameters of such level schemes can be tailored beyond those offered by the bare nuclei. However, so far, the direct determination of a cavity structure providing a desired quantum optical functionality has remained an open challenge. Here we address this challenge using an inverse design methodology. As a first qualitative result, we show that the established fitting approach based on scattering observables in general is not unique, since the analysis may lead to different multilevel systems for the same cavity if based on observables in different scattering channels. Motivated by this, we distinguish between scattering signatures and the microscopic level scheme as separate design objectives, with the latter being uniquely determined by an ab initio approach. We find that both design objectives are of practical relevance and that they complement each other regarding potential applications. We demonstrate the inverse design for both objectives using example tasks, such as realizing electromagnetically induced transparency. Our results pave the way for future applications in nuclear quantum optics involving more complex x-ray cavity designs.

DOI
10.1103/physreva.106.053701

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Ensembles of M"ossbauer nuclei embedded in thin-film cavities form a promising platform for x-ray quantum optics. A key feature is that the joint nuclei-cavity system can be considered as an artificial x-ray multilevel scheme in the low-excitation regime. Using the cavity environment, the structure and parameters of such level schemes can be tailored beyond those offered by the bare nuclei. However, so far, the direct determination of a cavity structure providing a desired quantum optical functionality has remained an open challenge. Here we address this challenge using an inverse design methodology. As a first qualitative result, we show that the established fitting approach based on scattering observables in general is not unique, since the analysis may lead to different multilevel systems for the same cavity if based on observables in different scattering channels. Motivated by this, we distinguish between scattering signatures and the microscopic level scheme as separate design objectives, with the latter being uniquely determined by an ab initio approach. We find that both design objectives are of practical relevance and that they complement each other regarding potential applications. We demonstrate the inverse design for both objectives using example tasks, such as realizing electromagnetically induced transparency. Our results pave the way for future applications in nuclear quantum optics involving more complex x-ray cavity designs.
Thin-film cavities containing layers of M\"ossbauer nuclei have been demonstrated to be a rich platform for x-ray quantum optics. At low excitation, these systems can be described by effective few-level schemes, thereby providing tunable artificial quantum systems at hard x-ray energies. With the recent advent of an ab initio theory, a numerically efficient description of these systems is now possible. On this basis, we introduce the inverse design and develop a comprehensive optimization for an archetypal system with a single resonant layer, corresponding to an artificial two-level scheme. We discover a number of qualitative insights into x-ray photonic environments for nuclei that will likely impact the design of future x-ray cavities and thereby improve their performance. The methods presented readily generalize beyond the two-level case and thus provide a clear perspective towards the inverse design of more advanced tunable x-ray quantum optical level schemes.
The setting of M\"ossbauer nuclei embedded in thin-film cavities has facilitated an aspiring platform for x-ray quantum optics as shown in several recent experiments. Here, we generalize the theoretical model of this platform that we developed earlier [Phys. Rev. A 88, 043828 (2013)]. The theory description is extended to cover multiple nuclear ensembles and multiple modes in the cavity. While the extensions separately do not lead to qualitatively new features, their combination gives rise to cooperative effects between the different nuclear ensembles and distinct spectral signatures in the observables. A related experiment by R\"ohlsberger et al. [Nature (London) 482, 199 (2012)] is successfully modeled, the scalings derived with semiclassical methods are reproduced, and a microscopic understanding of the setting is obtained with our quantum mechanical description.
In this thesis thin-film cavities with embedded Mössbauer nuclei probed by near-resonant x-ray light are studied from a quantum optical perspective. A theoretical framework is developed and compact expressions for the observables are derived for the linear excitation regime, which is encountered in current experiments. Even advanced cavity layouts can be modeled in excellent agreement with the results of previous experiments and semi-classical approaches. In the absence of magnetic hyperfine splitting, the spectral response of the system is found to be formed by tunable Fano profiles. An experimental implementation of this line shape control allows to extract spectroscopic signatures with high precision and to reconstruct the phase of the nuclear transition in good agreement with the theoretical predictions. The alignment of medium magnetization and polarization control of the x-rays enable to engineer advanced quantum optical level schemes, in which vacuum induced coherence effects are predicted and successfully demonstrated in an experiment. Furthermore, it is shown that group velocity control for x-ray pulses can be achieved in the cavity. A scheme for its observation is proposed and then employed to experimentally confirm sub-luminal x-ray propagation. Finally, non-linear effects, which could become accessible with future light sources, are explored and a non-linear line shape control mechanism is discussed.
A promising platform for the emerging field of x-ray quantum optics consists of M\"ossbauer nuclei embedded in thin-film cavities probed by near-resonant x-ray light, as used in a number of recent experiments. Here we develop a quantum optical framework for the description of experimentally relevant settings involving nuclei embedded in x-ray waveguides. We apply our formalism to two settings of current experimental interest based on the archetype M\"ossbauer isotope 57{}^{57}57Fe. For the present experimental conditions, we derive compact analytical expressions and show that the alignment of medium magnetization, as well as incident and detection polarization, enable the engineering of advanced quantum optical level schemes. The model encompasses nonlinear and quantum effects which could become accessible in future experiments.
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 M\"ossbauer nuclei such as 57Fe^{57}\mathrm{Fe}57Fe. 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.