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arXiv:0912.3979 · New Journal of Physics

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

XuanYang Lai, Qing-yu Cai, Minjie Zhan

Published Nov 20, 2009• 36 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1088/1367-2630/11/11/113035

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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 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.
The invention of lasers in the early sixties triggered the development of the rich field of nonlinear optics. Similarly, the development of lasers with ultrahigh intensities, that is, when the light electric field is larger than the attraction between electrons and nuclei, has boosted extreme nonlinear optics to a relevant and promising discipline in physics. Besides its technological potentialities, strong field physics is also challenging at a fundamental level, leading to the reconsideration of the basic processes of light-matter interactions. Also, the complexity of the exact solutions of the nonperturbative equations has encouraged the development of simple approaches based in semiclassical concepts that offer invaluable insight into the basic processes involved. In this sense, Bohmian trajectories offer an interesting extension of the semiclassical treatment, since their description is purely quantum and , yet, they retain the intuitiveness of a classical description. In this chapter we study the interaction of a hydrogen atom with short and intense laser pulses. By first using a simplified one-dimensional model, we show how Bohmian trajectories can be used in the calculation of the above-threshold ionization (ATI) and harmonic generation spectra. We also present a full three-dimensional (3D) model to study the interaction of an atom with beams bearing orbital angular momentum (OAM) and use the trajectories to gain physical insight into the absorption of angular momentum.
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.
Both the physical picture of the dynamics of atoms and molecules in intense infrared fields and its theoretical description use the concept of electron trajectories. Here, we address a key question which arises in this context: Are distinctly quantum features of these trajectories, such as the complex-valued coordinates, physically relevant in the classically allowed region of phase space, and what is their origin? First, we argue that solutions of classical equations of motion can account for quantum effects. To this end, we construct an exact solution to the classical Hamilton–Jacobi equation which accounts for dynamics of the wave packet, and show that this solution is physically correct in the limit ħ→0. Second, we show that imaginary components of classical trajectories are directly linked to the finite size of the initial wave packet in momentum space. This way, if the electronic wave packet produced by optical tunnelling in strong infrared fields is localised both in coordinate and momentum, its motion after tunnelling ipso facto cannot be described with purely classical trajectories – in contrast to popular models in the literature.