"Superluminal paradox" in wavepacket propagation and its quantum mechanical resolution

Abstract

We analyse in detail the reshaping mechanism leading to apparently "superluminal" advancement of a wave packet traversing a classically forbidden region. In the coordinate representation, a barrier is shown to act as an effective beamsplitter, recombining envelopes of the freely propagating pulse with various spacial shifts. Causality ensures that none of the constituent envelopes are advanced with respect to free propagation, yet the resulting pulse is advanced due to a peculiar interference effect, similar to the one responsible for "anomalous" values which occur in Aharonov's "weak measurements". In the momentum space, the effect is understood as a bandwidth phenomenon, where the incident pulse probes local, rather than global, analytical properties of the transmission amplitude T (p). The advancement is achieved when T (p) mimics locally an exponential behaviour, similar to the one occurring in Berry's "superoscillations". Seen in a broader quantum mechanical context, the "paradox" is but a consequence of an attempt to obtain "which way?" information without destroying the interference between the pathways of interest. This explains, to a large extent, the failure to adequately describe tunnelling in terms of a single "tunnelling time".

References in corpus (4)

• Superoscillation in speckle patterns
• Physical mechanism of superluminal traversal time: interference between multiple finite wave packets
• Are the 'weak measurements' really measurements?
• Interference mechanism of seemingly superluminal tunnelling

Cited by in corpus (13)

• The Wigner time delay for laser induced tunnel-ionization via the electron propagator
• The meaning of "anomalous weak values" in quantum and classical theories
• Weak measurements measure probability amplitudes (and very little else)
• The Quantum Cheshire Cat effect: Theoretical basis and observational implications
• Path probabilities for consecutive measurements, and certain "quantum paradoxes"
• The Salecker-Wigner-Peres clock, Feynman paths, and a tunnelling time that should not exist
• Speed-up and slow-down of a quantum particle
• The role of reflections in the generation of a time delay in strong field ionization
• Rotating Gaussian wave packets in weak external potentials
• Control of Arrival Time using Structured Wave Packets
• Interference effects in tunnelling of "cat" wave packet states
• Statistics of resonance and non-resonance tunnelling of fermionised cold atoms
• Wigner's friends, tunnelling times and Feynman's "only mystery of quantum mechanics"