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Journal of Physics Conference Series

Hydrodynamical description of strong field-driven electron dynamics

Pierre Botheron, Bernard Pons

Published Nov 5, 2012• 0 citations
Publisher

Abstract

We present the implementation of the Bohmian hydrodynamical formulation of quantum mechanics to the description of strong field-driven electron dynamics. We consider the case of one-dimensional hydrogenic atoms subjected to strong and short laser pulses as well as one-electron ion-atom collisions. The quantum trajectories clearly picture the dynamics and yield an accurate description of the observables.

DOI
10.1088/1742-6596/388/3/032019

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We present the implementation of the Bohmian hydrodynamical formulation of quantum mechanics to the description of strong field-driven electron dynamics. We consider the case of one-dimensional hydrogenic atoms subjected to strong and short laser pulses as well as one-electron ion-atom collisions. The quantum trajectories clearly picture the dynamics and yield an accurate description of the observables.
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.
Quantum hydrodynamics is a formulation of quantum mechanics based on the probability density and flux (current) density of a quantum system. It can be used to define trajectories which allow for a particle-based interpretation of quantum mechanics, commonly known as Bohmian mechanics. However, quantum hydrodynamics rests on the usual time-dependent formulation of quantum mechanics where time appears as a parameter. This parameter describes the correlation of the state of the quantum system with an external system -- a clock -- which behaves according to classical mechanics. With the Exact Factorization of a quantum system into a marginal and a conditional system, quantum mechanics and hence quantum hydrodynamics can be generalized for quantum clocks. In this article, the theory is developed and it is shown that trajectories for the quantum system can still be defined, and that these trajectories depend conditionally on the trajectory of the clock. Such trajectories are not only interesting from a fundamental point of view, but they can also find practical applications whenever a dynamics relative to an external time parameter is composed of "fast" and "slow" degrees of freedom and the interest is in the fast ones, while quantum effects of the slow ones (like a branching of the wavepacket) cannot be neglected. As an illustration, time- and clock-dependent trajectories are calculated for a model system of a non-adiabatic dynamics, where an electron is the quantum system, a nucleus is the quantum clock, and an external time parameter is provided, e.g. via an interaction with a laser field that is not treated explicitly.
This introduction presents an overview of the key concepts discussed in the subsequent chapters of this book. The book explains the historical development of Bohmian mechanics, Bohmian mechanics for single particle and for many particle systems. It discusses the dynamics of a single hydrogen atom interacting with a strong laser and presents a clear example on how a Bohmianthinking on superluminal velocities and nonlocal interactions helps in extending the quantum theory towards relativity and quantum field theory. The book also explains model nanoscale electron devices and their Bohmiancomputing development for knowing the ab initio quantum mechanical structure, energetics and thermodynamics of multiatoms systems. It deals with new cosmological models describing the accelerating universe in the spatially flat case. The book describes how many conceptual problems that appear in a description of gravity in quantum mechanical terms, such as the measurement problem and the problem of time, can be overcome by adopting a Bohmian perspective.
Recent realization of an intense quantum light, namely bright squeezed vacuum, opened a new perspective on quantum light-matter interaction. Several theoretical works have appeared based on coherent state expansions of quantum state of light to investigate non-classical driving of high-harmonic generation in atomic gases and solids, or free-electron dynamics, but their predictions surprisingly coincide with what one could expect from essentially classical interpretations of the light statistics. A deeper theoretical insight into the underlying physics is necessary for understanding of observed experimental findings and predicting emerging effects relying on this new configuration. Here we present a theoretical framework to describe tunneling driven by quantum light, where the properties of such light are captured by a statistical ensemble of classical fields via a hydrodynamic, also referred to as Bohmian, formulation. Generalizing the quasiclassical theory of non-adiabatic tunneling driven by classical light, a single tunneling event is described by a bundle of tunneling solutions, each driven by a classical field corresponding to one realization in the ensemble. Quantum statistics of light are thus imprinted on the measured current. Fully quantum description of light via the Bohmian trajectories of its field provides a perfect fit to the description of the electron (under-) above-barrier dynamics in terms of (complex quasiclassical) real classical trajectories, resulting in a consistent and elegant theoretical approach. To illustrate this, we consider BSV-induced electron transport from the tip to the surface in the tunneling microscope configuration demonstrating the transition from the multiphoton to the direct tunneling regime.
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.