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Chinese Physics Letters

Calculation of the Duration of the Atomic Tunneling Ionization in a Strong Electrostatic Field by Using Bohmian Trajectories Approach

Fu-Ming Guo, Ji-Gen Chen, Suyu Li, Yujun Yang

Published Jul 1, 2015• 1 citation
Publisher

Abstract

The duration of a bound electron tunneling through the barrier formed by atomic potential and electrostatic field is calculated by the Bohmian trajectories scheme. The time of the tunneling ionization decreases with the increase of the amplitude of the electrostatic field. By using the information about the position, velocity and force of the Bohmian trajectories, the dynamical process of tunneling through the barrier is investigated.

DOI
10.1088/0256-307x/32/7/073201

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The duration of a bound electron tunneling through the barrier formed by atomic potential and electrostatic field is calculated by the Bohmian trajectories scheme. The time of the tunneling ionization decreases with the increase of the amplitude of the electrostatic field. By using the information about the position, velocity and force of the Bohmian trajectories, the dynamical process of tunneling through the barrier is investigated.
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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 light-emission process by the recombination of an ionized electron with its parent ion is investigated by the Bohmian trajectory scheme, and the efficiency of light emission calculated by 20 Bohmian trajectories is qualitatively identical to that obtained by numerically solving the time-dependent Schr\"odinger equation. It is found that the efficiency of light emission by recombination is determined by the oscillation amplitude of the Bohmian particle's Coulomb acceleration. Along with the decrease of the energy of the incident Bohmian particle, the deepening of the ion's potential well, and the increase of the product factor of the bound-state and continuum-state populations, the oscillation amplitude of the particle's Coulomb acceleration increases.
The ionization dynamics of two-electron atom in an intense laser field is studied by the Bohmian mechanics (BM) theory, and the xenon atomic potential function is used as a model. The single ionization process and double ionization process are calculated by the BM theory and their results are in good agreement with those calculated by numerically solving the time-dependent Schrödinger equation. The analyses of the types, trajectories, and forces of Bohmian particles (BPs) undergoing the single and double ionizations indicate that the re-collision process accounts for a considerable proportion in the singly ionized cases. Furthermore, the analysis of the work done by the external force acting on the BPs shows that the quantum force plays an important role in the re-collision process. This work is helpful in understanding the ionization of two-electron atom in an intense laser field.