Interpretation of the Fano lineshape reversal in quantum waveguides

Fano lineshape parameter $\left(q\right)$ reversal is a proxy for interaction beyond the usual interference of indistinguishable quantum pathways. Reversal of the Fano parameter has been observed recently in quantum dots (QDs). We show that such a profile reversal may come about from the interaction of interloping over-the-top states (shape resonances) in the “nonresonant” channel with the QD bound states, interacting with the continuum channel (Feshbach resonances). Using this mechanism, we show that with minimal modifications of the QD parameters, we can affect the presence or absence of interloping resonances and hence lineshape profile reversal, as a way of coherence engineering.

Figure 1

(Color online) The electron transmission spectrum (C) through a QWG is modeled as a 2D structure with left and right leads and a rectangular QD (a). The first two interacting transverse modes are shown in (b), with open (closed) mode in solid (dashed) line. The profile reversal at an energy of $42\mathrm{meV}$ in the leads is from the interaction of an open-channel interlopper resonance with closed-channel Feshbach resonances (c). The positions of open-channel (solid) and closed-channel (dashed) resonances are indicated. The values of the Fano parameter $q$ are shown in (c) (full circles).

Figure 2

(Color online) A model QWG containing left and right leads coupled smoothly to a QD (a). The first two interacting transverse modes are shown in (b), with the open mode (solid line) and the closed mode (dashed line). The transmission spectrum (c) shows a series of resonance dips which correspond well to the positions of the bound states in the closed channel, as indicated. No reversal of the Fano profiles appears.

Figure 3

(Color online) A smooth QD coupled lead with a small perturbation (marked by arrows) (a), which introduces small barriers (marked by arrows) in the effective potential shown in (b). The transmission is fully affected by the perturbation (see Fig. 2), and in particular, produces a reversal of the Fano profiles. The values of $q$ are also shown on top of the transmission spectrum (c) (full circles). Large $\mid q\mid$ values are not shown. The sign of $q$, however, only changes after crossing $E\approx 53\mathrm{meV}$.