Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Chinese Physics B

Ionization of two-electron atom (xenon) studied by Bohmian mechanics theory*

Yang Song, Shu Han, Yujun Yang, Fu-Ming Guo, Suyu Li

Published Oct 26, 2020• 1 citation
Publisher

Abstract

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.

DOI
10.1088/1674-1056/abb22e

Related papers

Resonance-enhanced two-photon ionization of hydrogen atom in intense laser field investigated by Bohmian-mechanics*

Yang Song, Shu Han, Yujun Yang +2 more

Resonance enhanced two-photon ionization process of hydrogen atom via the resonant laser pulse is studied by Bohmian mechanics (BM) method. By analyzing the trajectories and energies of Bohmian particles (BPs), we find that under the action of high frequency and low intensity multi-circle resonant laser pulses, the ionized BPs first absorb one photon completing the excitation, and then absorb another photon, completing the ionization after staying in the first excited state for a period of time. The analysis of work done by the forces shows that the electric field force and quantum force play a major role in the whole ionization process. At the excitation moment and in the excitation-ionization process, the effect of the quantum force is greater than that of the electric field force. Finally, we discuss the principle of work and energy for BPs, and find that the electric field force and quantum force are non-conservative forces whose work is equal to the increment of mechanical energy of the system. In addition, it is proved that the quantum potential energy actually comes from the kinetic energy of the system and the increment of kinetic energy is equal to that of the kinetic energy of the system.

Chinese Physics B•Jun 29, 2020•1 citation

Revisiting the time-dependent ionization process through the Bohmian-mechanics method

Yang Song, Yujun Yang, Fu-Ming Guo +1 more

Abstract The ionization process of a hydrogen-like atom in the intense laser field is studied by the Bohmian-mechanics method. We propose a criterion for atomic ionization based on the total energy of a Bohmian particle (BP): when it is larger than or equal to zero, ionization occurs, when it is lower than zero, no ionization occurs. We find that the time-dependent ionization probabilities calculated by the Bohmian-mechanics and projection methods are almost the same under different laser parameters. Two typical Bohmian trajectories are selected to analyze the ionization process. The consistency between the time-dependent ionization probabilities calculated by the two methods is quantitatively analyzed from the aspect of the probability density of the wave-function.

Journal of Physics B Atomic Molecular and Optical Physics•Feb 27, 2017•11 citations

From a quantum to a classical description of intense laser–atom physics with Bohmian trajectories

XuanYang Lai, Qing-yu Cai, Minjie Zhan

In this paper, Bohmian mechanics is applied to intense laser–atom physics. The motion of an atomic electron in an intense laser field is obtained from the Bohm–Newton equation. We find that the quantum potential that dominates the quantum effect of a physical system becomes negligible as the electron is driven far from the parent ion by the intense laser field, i.e. the behavior of the electron smoothly tends towards classical soon after the electron is ionized. Our numerical calculations present direct positive evidence for semiclassical trajectory methods in intense laser–atom physics where the motion of the ionized electron is treated by classical mechanics, while quantum mechanics is needed before the ionization.

arXiv:0912.3979•New Journal of Physics•Nov 20, 2009•36 citations

Bohmian mechanics to high-order harmonic generation

XuanYang Lai, Qing-yu Cai, Mingsheng Zhan

This paper introduces Bohmian mechanics (BM) into the intense laser-atom physics to study high-order harmonic generation. In BM, the trajectories of atomic electron in an intense laser field can be obtained with the Bohm–Newton equation. The power spectrum with the trajectory of an atomic electron is calculated, which is found to be irregular. Next, the power spectrum associated with an atom ensemble from BM is considered, where the power spectrum becomes regular and consistent with that from quantum mechanics. Finally, the reason of the generation of the irregular spectrum is discussed.

arXiv:0911.1529•Chinese Physics B•Feb 1, 2010•16 citations

Bohmian mechanics in the exact factorization of electron-nuclear wave functions

Yasumitsu Suzuki, Kazuyuki Watanabe

The exact factorization of an electron-nuclear wave function [A. Abedi, N. T. Maitra, and E. K. U. Gross, Phys. Rev. Lett. 105, 123002 (2010)] allows us to define the rigorous nuclear time-dependent Schr\"odinger equation (TDSE) with a time-dependent potential-energy surface (TDPES) that fully accounts for the coupling to the electronic motion and drives the nuclear wave-packet dynamics. Here, we study whether the propagation of multiple classical trajectories can reproduce the quantum nuclear motion in strong-field processes when their motions are governed by the quantum Hamilton-Jacobi equation derived by applying Bohmian mechanics to this exact nuclear TDSE. We demonstrate that multiple classical trajectories propagated by the force from the gradient of the exact TDPES plus the Bohmian quantum potential can reproduce the strong-field dissociation dynamics of a one-dimensional model of the ${{\mathrm{H}}_{2}}^{+}$ molecule. Our results show that the force from the Bohmian quantum potential plays a non-negligible role in yielding quantum nuclear dynamics in the strong-field process studied here, where ionization and/or splitting of nuclear probability density occurs.

arXiv:1607.04854•Physical Review A•Sep 29, 2016•32 citations

Single-photon double ionization of an atom in a strong radiation field

Elena A. Volkova, A. M. Popov, Olga V. Tikhonova

Double ionization is studied by direct numerical integration of the time-dependent Schrödinger equation for a model two-electron system in the field of an electromagnetic wave in the case when the photon energy exceeds the energy required for the removal of both electrons of the atom. The probabilities of single-electron and double ionization are obtained as functions of the radiation intensity. The energy spectra and double pulse distributions of photoelectrons are analyzed. It is shown that single-photon ionization plays a significant role only in the limiting cases of weak and strong fields. The obtained results are used in an analysis of the contributions from different channels to the double-ionization process (in particular, for clarifying the role of the electron-electron interaction). The results of numerical calculations are compared with the analytic model of the phenomenon.

Journal of Experimental and Theoretical Physics•Mar 1, 2002•0 citations
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.
Resonance enhanced two-photon ionization process of hydrogen atom via the resonant laser pulse is studied by Bohmian mechanics (BM) method. By analyzing the trajectories and energies of Bohmian particles (BPs), we find that under the action of high frequency and low intensity multi-circle resonant laser pulses, the ionized BPs first absorb one photon completing the excitation, and then absorb another photon, completing the ionization after staying in the first excited state for a period of time. The analysis of work done by the forces shows that the electric field force and quantum force play a major role in the whole ionization process. At the excitation moment and in the excitation-ionization process, the effect of the quantum force is greater than that of the electric field force. Finally, we discuss the principle of work and energy for BPs, and find that the electric field force and quantum force are non-conservative forces whose work is equal to the increment of mechanical energy of the system. In addition, it is proved that the quantum potential energy actually comes from the kinetic energy of the system and the increment of kinetic energy is equal to that of the kinetic energy of the system.
Abstract The ionization process of a hydrogen-like atom in the intense laser field is studied by the Bohmian-mechanics method. We propose a criterion for atomic ionization based on the total energy of a Bohmian particle (BP): when it is larger than or equal to zero, ionization occurs, when it is lower than zero, no ionization occurs. We find that the time-dependent ionization probabilities calculated by the Bohmian-mechanics and projection methods are almost the same under different laser parameters. Two typical Bohmian trajectories are selected to analyze the ionization process. The consistency between the time-dependent ionization probabilities calculated by the two methods is quantitatively analyzed from the aspect of the probability density of the wave-function.
In this paper, Bohmian mechanics is applied to intense laser–atom physics. The motion of an atomic electron in an intense laser field is obtained from the Bohm–Newton equation. We find that the quantum potential that dominates the quantum effect of a physical system becomes negligible as the electron is driven far from the parent ion by the intense laser field, i.e. the behavior of the electron smoothly tends towards classical soon after the electron is ionized. Our numerical calculations present direct positive evidence for semiclassical trajectory methods in intense laser–atom physics where the motion of the ionized electron is treated by classical mechanics, while quantum mechanics is needed before the ionization.
This paper introduces Bohmian mechanics (BM) into the intense laser-atom physics to study high-order harmonic generation. In BM, the trajectories of atomic electron in an intense laser field can be obtained with the Bohm–Newton equation. The power spectrum with the trajectory of an atomic electron is calculated, which is found to be irregular. Next, the power spectrum associated with an atom ensemble from BM is considered, where the power spectrum becomes regular and consistent with that from quantum mechanics. Finally, the reason of the generation of the irregular spectrum is discussed.
The exact factorization of an electron-nuclear wave function [A. Abedi, N. T. Maitra, and E. K. U. Gross, Phys. Rev. Lett. 105, 123002 (2010)] allows us to define the rigorous nuclear time-dependent Schr\"odinger equation (TDSE) with a time-dependent potential-energy surface (TDPES) that fully accounts for the coupling to the electronic motion and drives the nuclear wave-packet dynamics. Here, we study whether the propagation of multiple classical trajectories can reproduce the quantum nuclear motion in strong-field processes when their motions are governed by the quantum Hamilton-Jacobi equation derived by applying Bohmian mechanics to this exact nuclear TDSE. We demonstrate that multiple classical trajectories propagated by the force from the gradient of the exact TDPES plus the Bohmian quantum potential can reproduce the strong-field dissociation dynamics of a one-dimensional model of the H2+{{\mathrm{H}}_{2}}^{+}H2​+ molecule. Our results show that the force from the Bohmian quantum potential plays a non-negligible role in yielding quantum nuclear dynamics in the strong-field process studied here, where ionization and/or splitting of nuclear probability density occurs.
Double ionization is studied by direct numerical integration of the time-dependent Schrödinger equation for a model two-electron system in the field of an electromagnetic wave in the case when the photon energy exceeds the energy required for the removal of both electrons of the atom. The probabilities of single-electron and double ionization are obtained as functions of the radiation intensity. The energy spectra and double pulse distributions of photoelectrons are analyzed. It is shown that single-photon ionization plays a significant role only in the limiting cases of weak and strong fields. The obtained results are used in an analysis of the contributions from different channels to the double-ionization process (in particular, for clarifying the role of the electron-electron interaction). The results of numerical calculations are compared with the analytic model of the phenomenon.