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Communications Physics

Unifying attoclock and Larmor measurements through position-resolved weak values

Pablo M. Maier, Serguei Patchkovskii, Misha Ivanov, Olga V. Smirnova

Published Apr 17, 2026• 1 citation
Publisher

Abstract

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.

DOI
10.1038/s42005-026-02615-6

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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.
Tunneling delays represent a hotly debated topic, with many conflicting definitions and little consensus on when and if such definitions accurately describe the physical observables. Here, we relate these different definitions to distinct experimental observables in strong field ionization, finding that two definitions, Larmor time and Bohmian time, are compatible with the attoclock observable and the resonance lifetime of a bound state, respectively. Both of these definitions are closely connected to the theory of weak measurement, with Larmor time being the weak measurement value of tunneling time and Bohmian trajectory corresponding to the average particle trajectory, which has been recently reconstructed using weak measurement in a two-slit experiment [S. Kocsis, B. Braverman, S. Ravets, M. J. Stevens, R. P. Mirin, L. K. Shalm, and A. M. Steinberg, Science 332, 1170 (2011)]. We demonstrate a big discrepancy in strong field ionization between the Bohmian and weak measurement values of tunneling time, and we suggest this arises because the tunneling time is calculated for a small probability postselected ensemble of electrons. Our results have important implications for the interpretation of experiments in attosecond science, suggesting that tunneling is unlikely to be an instantaneous process.
The measurement of the tunneling time-delay is hotly debated and remains controversial. In previous works, we showed that a model that accurately describes the time-delay measured by the attoclock experiment in adiabatic and nonadiabatic field calibrations. In the present work, we show that the tunneling time reveals a universal behavior with disentangled contributions. Even more remarkable is that the barrier tunneling time-delay can be convincingly defined and determined from the difference between the time-delay of adiabatic and nonadiabatic tunnel-ionization, which also show good agreement with experimental results. Furthermore, we illustrate that in the weak measurement limit, the barrier time-delay corresponds to the Larmor-clock time and the interaction time within the barrier.
Abstract The measurement of the tunneling time-delay is hotly debated and remains controversial. In previous works, we showed that a model that accurately describes the time-delay measured by the attoclock experiment in adiabatic and nonadiabatic field calibrations. In the present work, we show that the tunneling time reveals a universal behavior with disentangled contributions. Even more remarkable is that the barrier tunneling time-delay can be convincingly defined and determined from the difference between the time-delay of adiabatic and nonadiabatic tunnel-ionization, which also show good agreement with experimental results. Furthermore, we illustrate that in the weak measurement limit, the barrier time-delay corresponds to the Larmor-clock time and the interaction time within the barrier.
The measurement of the tunneling time-delay is hotly debated and remains controversial. In previous works, we showed that a model that accurately describes the time-delay measured by the attoclock experiment in adiabatic and nonadiabatic field calibrations. In the present work, we show that the tunneling time reveals a universal behavior with disentangled contributions. Even more remarkable is that the barrier tunneling time-delay can be convincingly defined and determined from the difference between the time-delay of adiabatic and nonadiabatic tunnel-ionization, which also show good agreement with experimental results. Furthermore, we illustrate that in the weak measurement limit, the barrier time-delay corresponds to the Larmor-clock time and the interaction time within the barrier.
Tunnelling lies at the heart of quantum mechanics and is a fundamental process in attosecond science, molecular biology, and quantum devices. Whether tunnelling takes time and how a microscopic particle transits through a barrier have been debated since the early days of quantum mechanics. The time required for an electron to tunnel through an atomic potential barrier has been measured with attosecond angular streaking (attoclock), and a recent work on the hydrogen atom claimed that electron tunnelling is instantaneous. However, the time required for Rb atoms to tunnel through an optical potential barrier has been measured to be on the order of milliseconds with a recent Larmor clock measurement. The essence of electron and atom tunnelling is identical, but the reason for the contradictory conclusions remains unknown. Here, we demonstrate that the sub-barrier potential interaction is the root of the nonzero tunnelling delay time. We reveal that the wave-particle duality of a tunnelling electron must be fully taken into account when decoding the tunnelling delay time from the attoclock measurements. Based on energy-resolved attoclock measurements, we show that the tunnelling delay time of an electron ranges from 24 to 58 attoseconds, and the counterintuitive result that an electron with a lower energy may spend less time in the barrier is consistent with the velocity-dependent tunnelling time of atoms in Larmor clock measurements. Our results unify the tunnelling time of microscopic particles by highlighting the classically forbidden sub-barrier potential interactions of matter waves.