Interference mechanism of seemingly superluminal tunneling

In the early 1930s MacColl [1] noticed that quantum tunneling appears to take no time or little time, in the sense that the peak of a wave packet, transmitted across a classically forbidden region, may arrive at a detector earlier than that of the freely propagating one. If the advanced peak is used to predict the time τ the particle has spent in the barrier region, the result is nearly zero. Dividing the barrier width by τ yields a velocity exceeding the speed of light c, suggesting that the transmission has a “superluminal” aspect. The effect has been predicted and observed for various systems such as potential barriers, semitransparent mirrors, refraction of light, and microwaves in undersized waveguides (for a review see Refs. [2–5]). Since below a barrier evanescent waves decay rather than propagate, it cannot be explained in terms of superluminal group velocities found, for example, in propagation in transparent media with inverted atomic populations [6].