Pulse Propagation in Resonant Tunneling II

TL;DR

This paper analyzes how Gaussian pulses tunnel through Fano resonances, showing that transmitted pulse data can uniquely determine resonance parameters and identifying two distinct propagation regimes based on resonance width.

Contribution

It provides an analytical model linking pulse transmission to Fano resonance parameters, contrasting with static conductance measurements, and identifies two propagation regimes with distinct behaviors.

Findings

Transmitted pulse contains enough information to determine Fano resonance parameters.

Broad resonances produce weakly deformed, slightly delayed pulses.

Narrow resonances lead to exponential decay and interference oscillations.

Abstract

We consider the analytically solvable model of a Gaussian pulse tunneling through a transmission resonance with a general Fano characteristic. It is demonstrated that the transmitted pulse contains enough information to determine uniquely all parameters defining the Fano resonance. This is in contrast to the measurement of the static conductance. Our analytical model is in agreement with numerical data published recently for the limit of a Breit-Wigner resonance. We identify two opposite pulse propagation regimes: if the resonance is broad compared to the energetic width of the incident Gaussian pulse a weakly deformed and slightly delayed transmitted Gaussian pulse is found. In the opposite limit of a narrow resonance the dying out of the transmitted pulse is dominated by the slow exponential decay characteristic of a quasi-bound state with a long life time. In this regime we find characteristic interference oscillations.