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Lasers in Engineering

Modified schrödinger equation for attosecond laser pulse interaction with matter

Janina Marciak-kozlowska B, Mirosław Kozłowski

Published Jan 1, 2002• 14 citations
Publisher

Abstract

Recently the measurement of X-ray pulses approaching the attosecond frontier was published (M. Drescher et al ., Science 291 (2001) p. 1923). The attosecond laser pulse enables the study and control of the motion of electrons inside atoms. In this paper we develop and solve the modified Schrödinger equation (MSE) which describes the interaction of electrons with its surroundings in an atom. This interaction can be detected only using an attosecond laser pulse within the relaxation time of the interaction which is of the order of 10 attoseconds.

DOI
10.1080/08981500290022770

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Recently the measurement of X-ray pulses approaching the attosecond frontier was published (M. Drescher et al ., Science 291 (2001) p. 1923). The attosecond laser pulse enables the study and control of the motion of electrons inside atoms. In this paper we develop and solve the modified Schrödinger equation (MSE) which describes the interaction of electrons with its surroundings in an atom. This interaction can be detected only using an attosecond laser pulse within the relaxation time of the interaction which is of the order of 10 attoseconds.
The past thirty years witnessed rapid developing of strong field physics that leads to the first generation of attosecond (10−18 s) pulses. The duration of available pulses has recently been reduced to less than 100 as, approaching the Kepler period of a classical electron revolving around the nucleus. For the first time, electron motions inside atoms, molecules and solids can be traced, probed and even steered in real time. It pushed the study on ultrafast dynamic processes into a new frontier, giving birth to attosecond physics. The development of attosecond pulses provides unprecedented coherent ultrashort XUV (extreme ultra-violet) of soft X-ray sources that enable imaging the atomic structure and resolving the related quantum dynamics for matter science. In particular, it allows the probing and monitoring of electron dynamics in the natural time scale of attoseconds with atomic spatial resolution. The generation and applications of attosecond pulses are directly related to the control and manipulation of the sub-cycle electron dynamics. Recent studies on the correlated multielectron dynamics have provided insight into the optical and dynamical properties of matter in the perspectives of time, phase and entanglement. It deepens our understanding on some of the fundamental questions, e.g., how the single or multiple photons are absorbed and how short are the quantum processes such as photoionization, tunneling ionization and charge migration. Although currently attosecond pulses are limited by the flux and pulse duration, the combination of attosecond pulses with intense infrared laser pulses paves new ways of controlling and probing electron dynamics in the domains of energy, time and space that lays the foundation for petahertz optoelectronics and attosecond pulse based transient spectroscopy. In this review, we will first briefly summarize the advancement of strong field and ultrafast physics including the relevant experimental findings, the theoretical explorations, the related technologies and the possible applications. Then we focus on the sub-cycle electron or multielectron dynamics and their manifestation on the ionization and coherent radiation properties. We start with the time behavior of Fano resonance and how it can be probed in time domain. In section 2, the correlated electron dynamics is discussed in term of anti-screening effect and Pauli effect that influence strong field ionization and high harmonic generation processes. In section 3, the coherent emission with frequency from terahertz to soft XUV and their joint measurement are discussed by emphasizing the generation mechanism of terahertz wave in two-color laser pulses. The developed high-harmonic and terahertz wave spectroscopy (HATS) is shown capable of imaging the molecular structure and dynamics. In section 4, the time-resolving of electron and hole dynamics and their coherence is proposed based on attosecond transient absorption technique. The coherence of ionization and the correlated electron dynamics is hinted crucial for electron-hole interaction. The topics are very limited and mainly selected from the perspectives of our group.
Until recently, attosecond optical spectroscopy and quantum optics evolved along non-overlapping directions. In attosecond science, attosecond pulses have been regarded as classical waves, applied to probe electron dynamics on their natural time scale. Here, we transfer fundamental concepts of quantum optics into attosecond physics, enabling control of both the properties of the XUV attosecond pulses and the quantum fluctuations of matter on attosecond time scales. By combining bright squeezed vacuum (BSV) with a strong laser field to drive high-harmonic generation, we transfer the quantum properties of the BSV onto the resulting XUV attosecond pulses. Applying advanced attosecond interferometry, we reconstruct the quantum state of the XUV high harmonics and their associated attosecond pulses with attosecond precision. Finally, we resolve the squeezing of the electron's wavepacket during one of the most fundamental strong-field phenomena - field induced tunneling. The ability to measure and control quantum correlations in both electrons and XUV attosecond pulses establishes a foundation for attosecond quantum electrodynamics, manipulating the quantum state of electrons and photons with sub-cycle precision.
To measure and control the electron motion in atoms and molecules by the strong laser field on the attosecond time scale is one of the research frontiers of atomic and molecular photophysics. It involves many new phenomena and processes and raises a series of questions of concepts, theories, and methods. Recent studies show that the Coulomb potential can cause the ionization time lag (about 100 attoseconds) between instants of the field maximum and the ionization-rate maximum. This lag can be understood as the response time of the electronic wave function to the strong-field-induced ionization event. It has a profound influence on the subsequent ultrafast dynamics of the ionized electron and can significantly change the time–frequency properties of electron trajectory (an important theoretical tool for attosecond measurement). Here, the research progress of response time and its implications on attosecond measurement are briefly introduced.
By solving the three-dimensional, time-dependent Schr\"odinger equation, we have demonstrated that the ultrafast charge-transfer process in ion-atom collisions can be mapped out with attosecond extreme uv (xuv) pulses. During the dynamic-charge transfer from the target atom to the projectile ion, the electron coherently populates the two sites of both nuclei, which can be viewed as a ``short-lived'' molecular state. A probing attosecond xuv pulse can instantly unleash the delocalized electron from such a ``transient molecule,'' so that the resulting photoelectron may exhibit a ``double-slit'' interference. On the contrary, either reduced or no photoelectron interference will occur if the attosecond xuv pulse strikes well before or after the collision. Therefore, by monitoring the photoelectron interference visibility, one can precisely time the ultrafast charge-transfer process in atomic collisions with time-delayed attosecond xuv pulses.
The advent of subfemtosecond or attosecond light pulses will open new fields of \nextreme nonlinear optics. Recently, experimental results on the production and \nmeasurement of a single 250-asec pulse were reported by Krausz et al [1]. This opens \nup new possibilities for studying and controlling electron dynamics in atoms and \nmolecules in asee time scale. Recently, Drescher et.al [2] has demonstrated that a \nlaser-based sampling system, consisting of a few-femtosecond visible light pulse and a \nasynchronized sub-femtosecond soft X-ray pulse, allows us to trace the relaxation \ndynamics directly in the time domain with attosecond resolution. Moreover, \nphotoionization and high-order harmonic generation (HHG) in molecular systems under \nthe action of combined infrared femtosecond and ultraviolet attosecond laser pulses \nwere investigated by Bandrauk and Shon [3]. It was shown that punctual "turn-on" of an \nasee pulse can trigger the ionization process, which in turn leads to significant \nenhancement of HHG. Despite the extensive work in this area, propagation of \nsubfemtosecond laser pulse has rarely been investigated.