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Superluminal tunneling times without superluminal signaling: Fading of the MacColl-Hartman effect at early times

Randall S. Dumont*

Tom Rivlin†

  • Department of Chemistry and Chemical Biology, McMaster University, Hamilton, Ontario, Canada L8S 4M1

  • Chemical and Biological Physics Department, Weizmann Institute of Science, 76100 Rehovot, Israel

  • *dumontr@mcmaster.ca
  • †Present address: Atominstitut, TU Wien, 1020 Vienna, Austria; tom.rivlin@tuwien.ac.at; tom.rivlin@weizman.ac.il
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Phys. Rev. A 107, 052212 – Published 19 May, 2023

DOI: https://doi.org/10.1103/PhysRevA.107.052212

Abstract

A curious feature of quantum tunneling known as the MacColl-Hartman effect results in the numerical observation that particles can traverse a barrier with effective superluminal speed. However, because tunneling is never certain, any attempt to use this effect to send a signal faster than light would require sending many particles. In this work, we consider sending—in parallel, without interactions between particles—sufficiently many particles to ensure at the least one of them tunnels. In this case, in spite of the time advance of the mean time for a single tunneling particle, the mean time to send one bit of information is larger for tunneling particles than for the same number of free photons. This removes any possibility of superluminal signaling. We show that the mean time to send one bit using N particles is determined by the early-time tail of the distribution of tunneling times for one particle and that, when this early-time tail is highly accurately modeled using steepest descent, the MacColl-Hartman effect is seen to fade away.

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Phys. Rev. A 107, 052212– Published 19 May, 2023
  • Received 26 January 2022
  • Revised 13 February 2023
  • Accepted 5 May 2023
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