Multiple Fano Resonances in Dynamic Resonant Tunneling Processes

The existence of Fano resonances in dynamic resonant tunneling (RT) systems has been investigated. Fano resonances are characterized by the appearance of a 100% reflection coefficient in proximity to a high transmission coefficient. For a Fano resonance to appear, a bound state must exist. On the other hand, a resonant tunneling process is characterized by a high transmission and the existence of a quasi-bound state (QBS) instead of a bound one. It has been shown that, by narrowing the width of the barrier, the resonance energy of the QBS gradually decreases and eventually turns into a bound state. Consequently, in a dynamic RT process, there are two scenarios: either a bound state exists, in which case, Fano resonances exist for any barrier width, or a QBS exists, and the barrier should be narrow enough for the Fano resonance to appear. In both cases, the incoming particle’s frequency must be lower than the oscillating well’s frequency. In this work, these resonances are investigated in detail, and both exactly numerically and approximated analytical expressions are derived for both the weak and strong oscillating amplitude regimes. One of the conclusions is that, when the oscillating frequency is low enough, multiple Fano resonances can appear by varying the barrier’s width. Since these resonances are very sharp and zero transmission can easily be detected, this property can be used as a very accurate method for measuring the barrier’s width, even when the particle’s de-Broglie wavelength is much larger than the barrier’s width.