Tunable Fano resonances in transport through microwave billiards

We present a tunable microwave scattering device that allows the controlled variation of Fano line shape parameters in transmission through quantum billiards. Transport in this device is nearly fully coherent. By comparison with quantum calculations, employing the modular recursive Green’s-function method, the scattering wave function and the degree of residual decoherence can be determined. The parametric variation of Fano line shapes in terms of interacting resonances is analyzed.

Figure 1

(Color online) (a) Schematic sketch of the rectangular cavity with leads attached symmetrically on opposite sides. Exchangeable diaphragms at the lead junctions allows one to control the coupling between the cavity and the leads. The open even transverse states are indicated. (b) Photograph of the experimental setup.

Figure 2

Total transmission probability $T^{\text{tot}}(\sqrt{2\epsilon }d∕\pi ,w∕d)$ for transport through the rectangular cavity with three different openings of the diaphragms: (a) $w∕d=37\%$, (b) $w∕d=56\%$, and (c) $w∕d=100\%$. For better comparison, the experimental and the calculated results are shown as mirror images. The positions of all eigenstates in the closed cavity are indicated by the gray tick marks. For all the calculated curves shown, a damping constant of $\kappa ={10}^{-4}$ was used.

Figure 3

Fano resonance near the second even excited transverse mode at $kd∕\pi \approx 1.5095$. Experimental and theoretical results for four different cavity openings $(w∕d)$ are shown. Curves with equal $w∕d$ ratio are displayed in the same line style (solid, dashed, dotted, and dash-dotted). For all calculated curves a damping factor $\kappa ={10}^{-4}$ was used, except for the additional gray dashed curve shown for which $\kappa ={10}^{-3}$ and $w∕d=0.68$.

Figure 4

(Color online) Real part of the asymmetry parameter $\mid \text{Re}\left(q\right)\mid$ as a function of the diaphragm opening $w∕d$. The data represent fits to the experiment. Solid circles $•$ (open triangles $▵$) correspond to resonances originating from the first (second) even cavity eigenstate. Typical wave functions ${\mid \psi (x,y)\mid }^2$ for these two classes of resonances are shown in the inset. The $•$ resonances always keep an $\mid \text{Re}\left(q\right)\mid >10$, above which the Fano resonances are very close to the Breit-Wigner line shape $\left[\text{Re}\left(q\right)=\infty \right]$. The $▵$ resonances undergo a complete evolution from Breit-Wigner to window type as $w∕d$ varies between 0 and 1.