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Physical Review Letters

First Observation of New Flat Line Fano Profile via an X-Ray Planar Cavity

Zi-Ru Ma, Xin‐Chao Huang, Tian-Jun Li, Hongchang Wang, Genchang Liu, Zhanshan Wang, Bo Li, W. B. Li, Lin‐Fan Zhu

Published Nov 16, 2022• 12 citations
Publisher

Abstract

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.

DOI
10.1103/physrevlett.129.213602

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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.
Fano resonance is a well-celebrated weak-coupling phenomenon whereby a small interaction between a discrete and a continuum of excited states leads to an interference between the respective two transition amplitudes, resulting in an asymmetric line shape in the excitation spectra. We present the strong-coupling phase of the Fano's model where the interaction is localized in a region $\ensuremath{\xi}$ that is smaller than the collective coupling between the discrete state and the continuum. We explore the behavior of the excitation probability $\ensuremath{\sigma}$ as a function of $\ensuremath{\xi}$, the ratio of the bare transition amplitudes, and the energy of the discrete state. In the strong-coupling phase, the spectral function of the discrete state splits up and produces up to three complete destructive interferences or zeros of $\ensuremath{\sigma}$ along with ultrasharp features. We also find that the discrete state does not have to lie within the continuum to produce the well-known weak-coupling profiles of $\ensuremath{\sigma}$ as long as the collective coupling is strong enough. In addition, we consider a broadened state instead of a continuum and present a method that exactly treats such cases by explicitly including the source of the broadening---a weak coupling to the continuum of environment states---in the model.
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 qqq, but also open up an avenue to study the decoherence processes via the Fano-Lorentz shape in the thin-film planar cavity.
In a wave resonant scattering process the interference of the continuous scattering amplitude with a discrete resonant state, both of the same undulatory nature, gives rise to a Fano resonance profile. We report experimental evidence of a new kind of Fano resonance, in which the continuous amplitude is of a different nature than that of the resonant wave. The continuous amplitude, of a electromagnetic nature, comes from the measurement process and induces a new type of prompt, or rapid, response of the system which we describe theoretically including this response as a direct process.
Asymmetric spectral line shapes are a hallmark of interference of a quasi-bound state with a continuum of states. Such line shapes are well known for multichannel systems, for example, in photoionization or Feshbach resonances in molecular scattering. On the other hand, in resonant single channel scattering, the signature of such interference may disappear due to the orthogonality of partial waves. Here, we show that probing the angular dependence of the cross section allows us to unveil asymmetric Fano profiles also in a single channel shape resonance. We observe a shift in the peak of the resonance profile in the elastic collisions between metastable helium and deuterium molecules with detection angle, in excellent agreement with theoretical predictions from full quantum scattering calculations. Using a model description for the partial wave interference, we can disentangle the resonant and background contributions and extract the relative phase responsible for the characteristic Fano-like profiles from our experimental measurements.
Fano resonance is a ubiquitous phenomenon, and it is commonly interpreted as a two-channel interference of the discrete and continuous channels. The present work investigates the Fano profile from a perspective of the temporal evolution of the wave function. By exciting the atom with a δ pulse and calculating the evolution of the wave function, the Fano formula is deduced. The results clearly show that the Fano resonance is of a three-channel interference, which is different from the traditional understanding. The three channels are revealed as the ground-continuum, ground-discrete-continuum, and a previously unmentioned third channel, i.e., ground-continuum-discrete-continuum. The present three-channel interpretation can be easily generalized to other physical systems, contributing to a deeper understanding of the Fano profile.