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

The thin-film planar cavity implanted in the Mossbauer 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 phi rather than cot phi in the framework of the initial Fano theory with phi 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.