Superluminal tunnelling through successive barriers: Does QM predict infinite group-velocities?

The phenomenon of one-dimensional non-resonant tunnelling is analyzed through two or more successive (opaque) potential barriers, separated by intermediate free regions, by exploiting the relevant solutions to the Schrödinger equation. The total traversal time has been shown to be independent not only of the barrier widths (the so-called ‘Hartman effect’), but also of the widths of the regions, indicating that the effective group velocity in these regions can be regarded as practically infinite. This prediction has been theoretically confirmed and generalized, as well as interpreted in terms of ‘super-oscillations’. A recent experiment by Longhi et al. supported these predictions by considering two successive gratings in an optical fiber, allowing for the simulation of tunnelling due to the known formal identity between the Schrödinger and Helmholtz equations. The implications of this phenomenon are significant in the context of quantum mechanics, as they potentially challenge conventional notions of tunnelling time and velocity, suggesting that superluminal and arbitrarily large group velocities can occur within certain conditions.