The Hartman effect and weak measurements "which are not really weak"

Abstract

We show that in wavepacket tunnelling localisation of the transmitted particle amounts to a quantum measurement of the delay it experiences in the barrier. With no external degree of freedom involved, the envelope of the wavepacket plays the role of the initial pointer state. Under tunnelling conditions such 'self measurement' is necessarily weak, and the Hartman effect just reflects the general tendency of weak values to diverge, as post-selection in the final state becomes improbable. We also demonstrate that it is a good precision, or 'not really weak' quantum measurement: no matter how wide the barrier d, it is possible to transmit a wavepacket with a width σ small compared to the observed advancement. As is the case with all weak measurements, the probability of transmission rapidly decreases with the ratio σ/d.

6 pages, 1 figure

References in corpus (5)

• Ultrasensitive Beam Deflection Measurement via Interferometric Weak Value Amplification
• Complex weak values in quantum measurement
• Salecker-Wigner-Peres clock and average tunneling times
• On causality, apparent 'superluminality' and reshaping in barrier penetration
• Accurate "superluminal" transmission via entanglement, superoscillations and quasi-Dirac distributions

Cited by in corpus (2)

• "Superluminal paradox" in wavepacket propagation and its quantum mechanical resolution
• Interference mechanism of seemingly superluminal tunnelling