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Mysteries, Puzzles, and Paradoxes in Quantum Mechanics

Larmor tunneling times in the two-phase representation

Jacek Jakiel

Published Jan 1, 1999• 0 citations
Publisher
DOI
10.1063/1.57861

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arXiv:2503.07859•Mar 10, 2025•0 citations
Abstract The measurement of tunneling times in strong-field ionization has been the topic of much controversy in recent years, with the attoclock and Larmor clock being two of the main contenders for correctly reproducing these times. While the non-zero Larmor tunneling time has been unambiguously detected, the tunneling time measured by the attoclock appears to vanish in tunnel ionization of a hydrogen atom. By expressing the attoclock as the weak value of temporal delay, we extend its meaning beyond the traditional setup and connect it to the weak-value interpretation of the Larmor clock. Our approach allows us to derive the position-resolved attoclock tunneling time. We show how this time, while non-zero at the tunnel exit, vanishes at the detector, far away from the atom. Formally, this means that the attoclock does not measure the “local” Larmor time, but instead a “non-local” time closely related to the phase time.
The measurement of tunneling times in strong-field ionization has been the topic of much controversy in recent years, with the attoclock and Larmor clock being two of the main contenders for correctly reproducing these times. By expressing the attoclock as the weak value of temporal delay, we extend its meaning beyond the traditional setup. This allows us to calculate the attoclock time for a static one-dimensional tunneling model consisting of a binding delta potential and a constant electric field. We apply the Steinberg weak-value interpretation of the Larmor clock. Using this definition, we obtain the position-resolved time density during tunnel ionization, yielding a non-zero Larmor tunneling time. Our model allows us to derive the analogue of the position-resolved attoclock tunneling time. While non-zero at the tunnel exit, it vanishes at the detector, far away from the atom. Formally, this means that the attoclock does not measure the "local" Larmor time, but instead a "non-local" time closely related to the phase time.