Resonant tunneling transients and decay for a one-dimensional double barrier potential

Abstract

Motivated by recent experimental work on quantum dots subjected to voltage pulses we consider a simple model to study the transition between off-resonance and on-resonance scattering states with the same incident energy in response to a sudden change in the well depth of a double barrier potential structure. The change displaces the real part of the resonance energy to coincide with the incident energy. The resonance buildup is not given by a pure exponential growth due to the interference between incident and resonance components represented by nearby poles, but the resonance lifetime is a relevant time scale. The reverse process (resonance depletion) that follows the opposite change in the well depth detunes the resonance level and the incident energy but, except for short and long time deviations, the decay is exponential with the lifetime of the displaced resonance. For a larger change in the well depth beyond a critical depth, trapping dominates rather than decay since the resonance becomes a bound state.