Trapping effects in wave-packet scattering in a double-quantum-dot Aharonov-Bohm interferometer

Abstract

An exact analytical solution for the time evolution of cutoff Gaussian wave packets scattered by a double-quantum-dot Aharonov-Bohm interferometer is derived to analyze the trapping effects of the molecular states of the system. Our analysis reveals that the formation and decay of a quasistationary state at the Fano resonance produces a monochromatic emission embedded in the transmitted packet, characterized by a dominant frequency ${\ensuremath{\Omega}}_{av}={\ensuremath{\varepsilon}}_{n}/\ensuremath{\hbar}$ with a finite time duration, where ${\ensuremath{\varepsilon}}_{n}$ is the Fano resonance energy. We demonstrate that the duration of this coherent emission can be extended by narrowing the Fano resonance with appropriate variations of the Aharonov-Bohm phase. This emission is switched off in the limit of zero width, where the localization of the associated molecular state occurs.