Ultrafast propagation of Schrödinger waves in absorbing media

A quantum effect in which the temporal peak of the particle's wave density arrives at different locations simultaneously was investigated. The simultaneous arrival due to absorption, unlike the Hartman effect, occurs for carrier frequencies under or above the cutoff, and for arbitrarily large distances. A physical realization was proposed by illuminating a two-level atom with a detuned laser. The results show that the corresponding relativistic equation holds the effect up to the relativistic causality limit.