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Journal of Physics B Atomic Molecular and Optical Physics

Theoretical study of attosecond chronoscopy of strong-field atomic photoionization

Andrey K. Kazansky, N M Kabachnik

Published Jun 23, 2008• 7 citations
Publisher

Abstract

A model which describes the time evolution of strong-field photoionization of atoms is presented. Based on the numerical solution of the non-stationary Schrodinger equation, the model allows one to predict and to interpret the results of experiments on double photoionization of atoms by a combined action of a very short (attosecond) XUV pulse and a few-cycle IR pulse of a powerful laser at various delay times between the two pulses. Depending on the binding energy of the ionized electron, two types of processes are considered. If the electron is tightly bound (Ne case), the XUV pulse ionizes the atom and shakes up another (outer) electron to an excited state, which is subsequently ionized by the strong IR field. For an atom with a weakly bound outer electron (Li case), the IR field ionizes the latter, while the XUV pulse, ionizing the inner shell, terminates (or suppresses) the strong-field ionization. In both cases the yield of doubly ionized ions strongly depends on the delay time between the two pulses, revealing 'steps', oscillations and other features which characterize the time evolution of the ionization process. The presented model describes qualitatively the results of recent experiments on Ne.

DOI
10.1088/0953-4075/41/13/135601

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A model which describes the time evolution of strong-field photoionization of atoms is presented. Based on the numerical solution of the non-stationary Schrodinger equation, the model allows one to predict and to interpret the results of experiments on double photoionization of atoms by a combined action of a very short (attosecond) XUV pulse and a few-cycle IR pulse of a powerful laser at various delay times between the two pulses. Depending on the binding energy of the ionized electron, two types of processes are considered. If the electron is tightly bound (Ne case), the XUV pulse ionizes the atom and shakes up another (outer) electron to an excited state, which is subsequently ionized by the strong IR field. For an atom with a weakly bound outer electron (Li case), the IR field ionizes the latter, while the XUV pulse, ionizing the inner shell, terminates (or suppresses) the strong-field ionization. In both cases the yield of doubly ionized ions strongly depends on the delay time between the two pulses, revealing 'steps', oscillations and other features which characterize the time evolution of the ionization process. The presented model describes qualitatively the results of recent experiments on Ne.
Attosecond chronoscopy enables the exploration of correlated electron dynamics in real time. One key observable of attosecond physics is the determination of "time zero" of photoionization, the time delay with which the wave packet of the ionized electron departs from the ionic core. This observable has become accessible by experimental advances in attosecond streaking and reconstruction of attosecond beating by interference of two-photon transitions (RABBIT) techniques. In this Letter, we explore photoionization time delays by strong extreme ultraviolet fields beyond the linear-response limit. We identify novel signatures in time delays signifying strong coupling between atoms and light fields and the light-field dressing of the ion. As a prototypical case, we study the interelectronic coherence and entanglement in helium driven by a strong extreme ultraviolet field. By the numerical solution of the time-dependent Schrödinger equation in its full dimensionality, we show that the time delay of the photoionized electron allows one to monitor the ultrafast variations of coherence dynamics and entanglement in real time.
Based on the numerical solutions of the time-dependent Schrödinger equation within the single-active-electron approximation, we propose a method for observing instantaneous atomic level shifts in an oscillating strong infrared (IR) field with sub-IR-cycle time resolution, by using a single tunable attosecond (SA) pulse to probe excited states of the perturbed atom. The ionization probability in the combined fields depends on both the frequency of the attosecond pulse and the time delay between both pulses, since the IR field periodically shifts SA-pulse-excited energy levels into and out of resonance.
We calculate resonant absorption line shapes in helium atoms subject to the combination of an attosecond pulse of XUV radiation and a delayed, few-cycle infrared (IR) laser pulse. We are in particular interested in how the resonant features evolve with the delay between the fields and with increasing IR intensity. We first compare the single-atom absorption calculated by a nonperturbative solution of the time-dependent Schr\"odinger equation (TDSE) to a simple model in which the resonant absorption is modified only by a laser-imposed phase (LIP) that originates in the instantaneous ac Stark shift of the resonant state. We find that the LIP model can explain many features of the resonant absorption, including the direction of the resonance energy shift and the onset of dispersive line shapes with increasing IR intensity. We also find, however, that the LIP model predicts the energy shifts and the line shapes only qualitatively when the resonant states are strongly IR coupled to nearby states. We then use a coupled solution of the Maxwell wave equation and the TDSE to examine how the line shapes are modified by propagation effects at helium densities such that the resonant absorption is strong. We find that when the resonant absorption saturates, their line shapes are strongly modified due to reshaping of the attosecond pulse time profile during propagation. This in turn alters the ultrafast absorption and emission dynamics.
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.
The strong coupling between two autoionizing states in helium is studied theoretically with the pump-probe scheme. An isolated 100-as XUV pulse is used to excite helium near the 2s2p(1P)2s2p{(}^{1}\phantom{\rule{0.16em}{0ex}}P)2s2p(1P) resonance state in the presence of an intense infrared (IR) laser. The laser field introduces strong coupling between 2s2p(1P)2s2p{(}^{1}\phantom{\rule{0.16em}{0ex}}P)2s2p(1P) and 2p2(1S)2{p}^{2}{(}^{1}\phantom{\rule{0.16em}{0ex}}S)2p2(1S) states. The IR also can ionize helium from both autoionizing states. By changing the time delay between the XUV and the IR pulses, we investigated the photoelectron spectra near the two resonances. The results are used to explain the recent experiment by Gilbertson et al. [Phys. Rev. Lett. 105, 263003 (2010)]. Using the same isolated attosecond pulse and a 540-nm laser, we also investigate the strong coupling between 2s2p(1P)2s2p{(}^{1}\phantom{\rule{0.16em}{0ex}}P)2s2p(1P) and 2s2(1S)2{s}^{2}{(}^{1}\phantom{\rule{0.16em}{0ex}}S)2s2(1S) by examining how the photoelectron spectra are modified versus the time delay and the possibility of observing Autler-Townes doublet in such experiments.
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.