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Journal of Physics Conference Series

Distribution of ionization and tunneling times in a model of strong field ionization

Jose Tadeu Lunardi, Luiz A. Manzoni

Published Nov 1, 2019• 1 citation
Publisher

Abstract

Abstract We consider a simple model for strong field ionization and use the Salecker-Wigner-Peres clock to obtain a distribution of (real) times associated with this phenomenon. By coupling the Salecker-Wigner-Peres clock to the particle in different regions, we are able to distinguish between the ionization (exit) time, the tunneling time and the time the particle spends in the well before entering the barrier (the well time). We show that the distribution of ionization/exit times, which are the times usually measured in attoclock experiments, may differ significantly from the distribution of tunneling times, suggesting that the ionization times cannot be generally interpreted as tunneling times.

DOI
10.1088/1742-6596/1391/1/012112

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Abstract We consider a simple model for strong field ionization and use the Salecker-Wigner-Peres clock to obtain a distribution of (real) times associated with this phenomenon. By coupling the Salecker-Wigner-Peres clock to the particle in different regions, we are able to distinguish between the ionization (exit) time, the tunneling time and the time the particle spends in the well before entering the barrier (the well time). We show that the distribution of ionization/exit times, which are the times usually measured in attoclock experiments, may differ significantly from the distribution of tunneling times, suggesting that the ionization times cannot be generally interpreted as tunneling times.
We propose a general expression for the probability distribution of real-valued tunneling times of a localized particle, as measured by the Salecker-Wigner-Peres quantum clock. This general expression is used to obtain the distribution of times for the scattering of a particle through a static rectangular barrier and for the tunneling decay of an initially bound state after the sudden deformation of the potential, the latter case being relevant to understand tunneling times in recent attosecond experiments involving strong field ionization.
We propose a general expression for the probability distribution of real-valued tunneling times of a localized particle, as measured by the Salecker-Wigner-Peres quantum clock. This general expression is used to obtain the distribution of times for the scattering of a particle through a static rectangular barrier and for the tunneling decay of an initially bound state after the sudden deformation of the potential, the latter case being relevant to understand tunneling times in recent attosecond experiments involving strong field ionization.
The Salecker-Wigner-Peres quantum-clock approach is applied in order to determine the tunneling time of an electron in strong-field tunnel ionization via a time-dependent electric field. Our results show that the ionization of the electron takes a nonvanishing period of time. This tunneling time is of the order of the Keldysh time but strictly larger than the Keldysh time. Comparing the quantum-clock tunneling time to the mean tunneling time as obtained by the virtual-detector approach, one finds that these two complementary methods give very similar results. Due to the asymmetric distribution of the tunneling time, there is a nonnegligible discrepancy between the mean tunneling time and the most probable tunneling 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.
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.
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.