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Physical Review A

Fano-Lorentz shape controlled by the collective effect of the nuclear ensemble

Tian-Jun Li, Xin‐Chao Huang, Zi-Ru Ma, Bo Li, Xiyuan Wang, Lin‐Fan Zhu

Published Sep 26, 2023• 4 citations
Publisher

Abstract

The thin-film planar cavity implanted in the $\mathrm{M}\stackrel{\ifmmode \ddot{}\else \"{}\fi{}}{\mathrm{o}}\mathrm{ssbauer}$ nuclei has been developed as a powerful platform to study the light-matter interaction in the x-ray band. Herein the asymmetric and symmetric profiles of Fano interference are studied by controlling the collective effect and modifying the cavity structure. It is found that the asymmetric profiles in the overcritical and undercritical regimes are the Fano-Lorentz shape, and the asymmetry of the profile is determined by $\mathrm{cos}\ensuremath{\varphi}$ rather than $\mathrm{cot}\ensuremath{\varphi}$ in the framework of the initial Fano theory with $\ensuremath{\varphi}$ being the phase shift of the continuum. In addition, the Fano-Lorentz profile not only can be controlled by the phase difference of the two pathways, but also can be adjusted by the weight of the normal Fano resonance in the Fano-Lorentz profile through regulating the collective effect of the nuclear ensemble. By varying the nuclear abundance at the cavity mode angle, the transformation between the symmetric peak and valley is observed in the overcritical regime, whereas the symmetric peaks are always presented in the undercritical regime. Furthermore, a particularly interesting phenomenon of a flat reflectivity, as if the resonant nuclear ensemble is not excited, is predicted in the nuclear ensemble at a critical nuclear abundance in the overcritical regime. The present results will not only confirm the presence of the complex $q$, but also open up an avenue to study the decoherence processes via the Fano-Lorentz shape in the thin-film planar cavity.

DOI
10.1103/physreva.108.033715

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The thin-film planar cavity implanted in the Mo\ifmmode¨\else¨\fissbauer\mathrm{M}\stackrel{\ifmmode \ddot{}\else \"{}\fi{}}{\mathrm{o}}\mathrm{ssbauer}Mo\ifmmode¨\else¨\fissbauer nuclei has been developed as a powerful platform to study the light-matter interaction in the x-ray band. Herein the asymmetric and symmetric profiles of Fano interference are studied by controlling the collective effect and modifying the cavity structure. It is found that the asymmetric profiles in the overcritical and undercritical regimes are the Fano-Lorentz shape, and the asymmetry of the profile is determined by cos\ensuremathφ\mathrm{cos}\ensuremath{\varphi}cos\ensuremathφ rather than cot\ensuremathφ\mathrm{cot}\ensuremath{\varphi}cot\ensuremathφ in the framework of the initial Fano theory with \ensuremathφ\ensuremath{\varphi}\ensuremathφ being the phase shift of the continuum. In addition, the Fano-Lorentz profile not only can be controlled by the phase difference of the two pathways, but also can be adjusted by the weight of the normal Fano resonance in the Fano-Lorentz profile through regulating the collective effect of the nuclear ensemble. By varying the nuclear abundance at the cavity mode angle, the transformation between the symmetric peak and valley is observed in the overcritical regime, whereas the symmetric peaks are always presented in the undercritical regime. Furthermore, a particularly interesting phenomenon of a flat reflectivity, as if the resonant nuclear ensemble is not excited, is predicted in the nuclear ensemble at a critical nuclear abundance in the overcritical regime. The present results will not only confirm the presence of the complex qqq, but also open up an avenue to study the decoherence processes via the Fano-Lorentz shape in the thin-film planar cavity.
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In the absence of time-reversal symmetry, the asymmetric parameter q of the Fano resonance is extended into the complex space, where its trajectory can be utilized to investigate the decoherence process. By embedding the ensemble of Mo¨\ddot{\rm{o}}o¨ssbauer nuclei in the thin-film planar cavity in this work, the trajectories of asymmetric parameter q are studied via the collective effect of the nuclear ensemble, which is regulated by the nuclear abundance and angle offset. Due to the diverse controllable methods of the collective resonant strength, there are different straight lines and arc-shape trajectories in the complex plane, in which the slopes and the radius can be respectively adjusted by the angle offset and nuclear abundance. It is demonstrated that the dissipation process can be suppressed equivalently by the strong energy exchange between the cavity and nuclear ensemble. The present results could enrich the behaviors of the asymmetric parameter q in the complex plane and would provide new possibility for the decoherence research through the thin-film planar cavity.
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.
Symmetric Lorentzian and asymmetric Fano line shapes are fundamental spectroscopic signatures that quantify the structural and dynamical properties of nuclei, atoms, molecules, and solids. This study introduces a universal temporal-phase formalism, mapping the Fano asymmetry parameter q to a phase φ of the time-dependent dipole response function. The formalism is confirmed experimentally by laser-transforming Fano absorption lines of autoionizing helium into Lorentzian lines after attosecond-pulsed excitation. We also demonstrate the inverse, the transformation of a naturally Lorentzian line into a Fano profile. A further application of this formalism uses quantum-phase control to amplify extreme-ultraviolet light resonantly interacting with He atoms. The quantum phase of excited states and its response to interactions can thus be extracted from line-shape analysis, with applications in many branches of spectroscopy.
A new Fano profile of a flat line is achieved experimentally by manipulating the relative amplitude of the continuum path, when q takes the pure imaginary number of -i in the x-ray regime. The underlying mechanism is that the interference term in the scattering will cancel the discrete term exactly. This new Fano profile renders only an observable continuum along with an invisible response to the discrete state of atomic resonance. The results suggest not only a different strategy to invisibility studies which provides a possible tool to identify weaker structures hidden by the strong white line, but also a new scenario to enrich the manipulations of two-path interference and nonlinear Fano resonance.
Abstract Mössbauer nuclei with quadrupole-split levels provide a versatile platform for exploring coherent x-ray light-matter interactions. We theoretically study ensembles of 57 Fe nuclei embedded in thin-film x-ray cavities, explicitly accounting for different orientations of the electric field gradient. By mapping isotropic electric field gradient distributions to an effective equal-weight two-transition model, we derive analytical expressions for the time-dependent reflectivity and reveal the emergence of cavity-mediated quantum beats. The oscillation frequency and temporal profile of these beats can be tuned via the cavity-induced coherent coupling, offering a flexible approach to control collective nuclear dynamics and manipulate nuclear coherence in the x-ray regime.