We investigate the effect of decoherence on Fano resonances in wave transmission through resonant scattering structures. We show that the Fano asymmetry parameter q follows, as a function of the strength of decoherence, trajectories in the complex plane that reveal detailed information on the underlying decoherence process. Dissipation and unitary dephasing give rise to manifestly different trajectories. Our predictions are successfully tested against microwave experiments using metal cavities with different absorption coefficients and against previously published data on transport through quantum dots. These results open up new possibilities for studying the effect of decoherence in a wide array of physical systems where Fano resonances are present.
Abstract Realizing and controlling a Fano resonance is of fundamental significance in physics and may find applications in optical switching and sensitivity-enhanced biochemical sensing. Here we present a practicable scheme to realize Fano resonance and slow light in a quadratically coupled optomechanical system with membranes. It is shown that Fano resonance generation is precisely controlled by changing the frequency detuning between the cavity field and the control field in the quadratically coupled optomechanical system, while additional membrane inside the system can considerably establish a tunable switch between a single Fano resonance and double Fano resonances. In particular, the asymmetric line shape and the number of Fano resonance can be well tuned by the reflectivity of the membranes, the wavelength of the control field and the environment temperature. Furthermore, it is also shown that the slow light effects of the transmitted probe field can be obtained under two-phonon resonance condition and the group delay of the transmitted probe field can be adjusted by the frequency and power of the control field. Our scheme may help to achieve the practical application of Fano resonances relevant to the nonlinear optics.
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 M$\stackrel{\ifmmode \ddot{}\else \"{}\fi{}}{\mathrm{o}}$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-shaped trajectories in the complex plane, in which the slopes and the radius can be adjusted by the angle offset and nuclear abundance, respectively. It is demonstrated that the dissipation process can be ``suppressed'' equivalently by the strong energy exchange between the cavity and the nuclear ensemble. The present results could enrich the behaviors of the asymmetric parameter
q in the complex plane and would provide a new opportunity for decoherence research through the thin-film planar cavity.