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In the absence of time-reversal symmetry, the asymmetric parameter q of theFano resonance is extended into the complex space, where its trajectory can beutilized to investigate the decoherence process. By embedding the ensemble ofM$\ddot{\rm{o}}$ssbauer nuclei in the thin-film planar cavity in this work, thetrajectories of asymmetric parameter q are studied via the collective effect ofthe nuclear ensemble, which is regulated by the nuclear abundance and angleoffset. Due to the diverse controllable methods of the collective resonantstrength, there are different straight lines and arc-shape trajectories in thecomplex plane, in which the slopes and the radius can be respectively adjustedby the angle offset and nuclear abundance. It is demonstrated that thedissipation process can be suppressed equivalently by the strong energyexchange between the cavity and nuclear ensemble. The present results couldenrich the behaviors of the asymmetric parameter q in the complex plane andwould provide new possibility for the decoherence research through thethin-film planar cavity.

Probing dissipation process via Fano resonance and collective effect in the X-ray cavity