Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical Review A

Classical, semiclassical, and quantum-optical models for an x-ray planar cavity with electronic resonance

Xin‐Chao Huang, Tian-Jun Li, Frederico A. Lima, Lin‐Fan Zhu

Published Mar 4, 2024• 4 citations
Publisher

Abstract

Two theoretical models of semiclassical matrix method and quantum Green's function are extended to the system of x-ray thin-film planar cavity with inner-shell electronic resonances. The semiclassical model is based on the matrix formalism by treating each layer as the propagating matrix. The crucial idea is to expand the propagating matrix of the resonant atomic layer under ultrathin-film approximation, and then derive the analytical expression of the spectral observation, i.e., the cavity reflectance. Typical cavity-enhanced decay rate and cavity-induced energy shift as well as the Fano interference which were observed in recent experiments could be phenomenologically interpreted. The quantum model employs analytical Green's function to calculate the cavity system. The system Hamiltonian and the effective energy-level are derived. The effective energy-level scheme indicates that the cavity effect can control intermediate core-hole state. To test the validity of the semiclassical matrix and quantum Green's function models, the classical Parratt's formalism and the dispersion correction of the atomic refractive index are also recalled. Very good agreements in the reflectivity spectra between the semiclassical and quantum models with Parratt's results are observed. The equivalence between the matrix and Green's function models is discussed analytically and numerically. Based on these two theoretical models, the similarities and particularities of inner-shell electronic system are discussed and compared with the nuclear system. Several examples, including the weaker dipole moment, distorted Fano lineshape, and negligible collective effect, are given. The present semiclassical matrix and quantum Green's function models will be useful to predict new phenomena, to optimize cavity structure for future experiments, and to promote the emerging of x-ray quantum optical effects with modern x-ray spectroscopy techniques.

DOI
10.1103/physreva.109.033703

Related papers

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

Xiangjin Kong, Darrick E. Chang, Adriana Pálffy

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 $^{57}\mathrm{Fe}$. 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.

arXiv:2010.00249•Physical Review A•Sep 10, 2020•17 citations

X-Ray Quantum Optics With Mössbauer Nuclei In Thin-Film Cavities

Kilian P. Heeg

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.

•Jan 1, 2014•0 citations

Collective effects between multiple nuclear ensembles in an x-ray cavity-QED setup

Kilian P. Heeg, Jörg Evers

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.

arXiv:1504.02709•Physical Review A•Jun 3, 2015•29 citations

Spacing-dependent electromagnetically induced transparency with two nuclear ensembles inside an x-ray planar cavity

Xin‐Chao Huang, Zi-Ru Ma, Xiangjin Kong +2 more

The x-ray planar cavity embedded in two nuclear ensembles at node and antinode positions with fixed spacing has been used to study the electromagnetically induced transparency (EIT)-like effect previously. In this work, the same x-ray planar cavity but with a flexible spacing configuration is studied theoretically. By developing a concise transfer matrix method, the changing of spacing is reflected conveniently as the phase shift of the propagation matrices, based on which the system can be solved analytically. A periodic characteristic as a function of the spacing is observed, i.e., the first nuclear ensemble locating at any node will result in an EIT effect while the EIT effect will be completely compressed when it is at any antinode. It indicates that the phase shift between the two nuclear ensembles plays a key role for the coupling field. This kind of phase manipulation will enrich the approaches of quantum control in the x-ray regime.

Journal of the Optical Society of America B•Jan 13, 2020•6 citations

Inverse design approach to x-ray quantum optics with Mössbauer nuclei in thin-film cavities

Oliver Diekmann, Dominik Lentrodt, Jörg Evers

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.

arXiv:2108.01960•Physical Review A•Jan 21, 2022•15 citations

X-ray quantum optics with Mössbauer nuclei embedded in thin-film cavities

Kilian P. Heeg, Jörg Evers

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 ${}^{57}$Fe. 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.

arXiv:1305.4239•Physical Review A•Oct 15, 2013•58 citations
Two theoretical models of semiclassical matrix method and quantum Green's function are extended to the system of x-ray thin-film planar cavity with inner-shell electronic resonances. The semiclassical model is based on the matrix formalism by treating each layer as the propagating matrix. The crucial idea is to expand the propagating matrix of the resonant atomic layer under ultrathin-film approximation, and then derive the analytical expression of the spectral observation, i.e., the cavity reflectance. Typical cavity-enhanced decay rate and cavity-induced energy shift as well as the Fano interference which were observed in recent experiments could be phenomenologically interpreted. The quantum model employs analytical Green's function to calculate the cavity system. The system Hamiltonian and the effective energy-level are derived. The effective energy-level scheme indicates that the cavity effect can control intermediate core-hole state. To test the validity of the semiclassical matrix and quantum Green's function models, the classical Parratt's formalism and the dispersion correction of the atomic refractive index are also recalled. Very good agreements in the reflectivity spectra between the semiclassical and quantum models with Parratt's results are observed. The equivalence between the matrix and Green's function models is discussed analytically and numerically. Based on these two theoretical models, the similarities and particularities of inner-shell electronic system are discussed and compared with the nuclear system. Several examples, including the weaker dipole moment, distorted Fano lineshape, and negligible collective effect, are given. The present semiclassical matrix and quantum Green's function models will be useful to predict new phenomena, to optimize cavity structure for future experiments, and to promote the emerging of x-ray quantum optical effects with modern x-ray spectroscopy techniques.
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.
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.
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.
The x-ray planar cavity embedded in two nuclear ensembles at node and antinode positions with fixed spacing has been used to study the electromagnetically induced transparency (EIT)-like effect previously. In this work, the same x-ray planar cavity but with a flexible spacing configuration is studied theoretically. By developing a concise transfer matrix method, the changing of spacing is reflected conveniently as the phase shift of the propagation matrices, based on which the system can be solved analytically. A periodic characteristic as a function of the spacing is observed, i.e., the first nuclear ensemble locating at any node will result in an EIT effect while the EIT effect will be completely compressed when it is at any antinode. It indicates that the phase shift between the two nuclear ensembles plays a key role for the coupling field. This kind of phase manipulation will enrich the approaches of quantum control in the x-ray regime.
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.
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.