Summary form only given. Fundamental processes in atoms, molecules, as well as condensed matter are triggered or mediated by the motion of electrons inside or between atoms. Electronic dynamics on atomic length scales tends to unfold within tens to thousands of attoseconds (1 attosecond [as] = 10-18 s). Recent breakthroughs in laser science are now opening the door to watching and controlling these hitherto inaccessible microscopic dynamics. The key to accessing the attosecond time domain is the control of the electric field of (visible) light, which varies its strength and direction within less than a femtosecond (1 femtosecond = 1000 attoseconds). Atoms exposed to a few oscillations cycles of intense laser light are able to emit a single extreme ultraviolet (XUV) burst lasting less than one femtosecond. Full control of the evolution of the electromagnetic field in laser pulses comprising a few wave cycles have recently allowed the reproducible generation and measurement of isolated sub-femtosecond XUV pulses, demonstrating the control of microscopic processes (electron motion and photon emission) on an attosecond time scale. These tools have enabled us to visualize the oscillating electric field of visible light with an attosecond "oscilloscope", to control single-electron and probe multi-electron dynamics in atoms, molecules and solids. Recent experiments hold promise for the development of an attosecond X-ray source, which may pave the way towards 4D electron imaging with sub-atomic resolution in space and time.

Attosecond Physics

We generated single-cycle isolated attosecond pulses around ∼36 electron volts using phase-stabilized 5-femtosecond driving pulses with a modulated polarization state. Using a complete temporal characterization technique, we demonstrated the compression of the generated pulses for as low as 130 attoseconds, corresponding to less than 1.2 optical cycles. Numerical simulations of the generation process show that the carrier-envelope phase of the attosecond pulses is stable. The availability of single-cycle isolated attosecond pulses opens the way to a new regime in ultrafast physics, in which the strong-field electron dynamics in atoms and molecules is driven by the electric field of the attosecond pulses rather than by their intensity profile.

https://science.sciencemag.org/content/sci/314/5798/443.full.pdf

Isolated Single-Cycle Attosecond Pulses

For the past several decades, we have been able to directly probe the motion of atoms that is associated with chemical transformations and which occurs on the femtosecond (10(-15)-s) timescale. However, studying the inner workings of atoms and molecules on the electronic timescale has become possible only with the recent development of isolated attosecond (10(-18)-s) laser pulses. Such pulses have been used to investigate atomic photoexcitation and photoionization and electron dynamics in solids, and in molecules could help explore the prompt charge redistribution and localization that accompany photoexcitation processes. In recent work, the dissociative ionization of H(2) and D(2) was monitored on femtosecond timescales and controlled using few-cycle near-infrared laser pulses. Here we report a molecular attosecond pump-probe experiment based on that work: H(2) and D(2) are dissociatively ionized by a sequence comprising an isolated attosecond ultraviolet pulse and an intense few-cycle infrared pulse, and a localization of the electronic charge distribution within the molecule is measured that depends-with attosecond time resolution-on the delay between the pump and probe pulses. The localization occurs by means of two mechanisms, where the infrared laser influences the photoionization or the dissociation of the molecular ion. In the first case, charge localization arises from quantum mechanical interference involving autoionizing states and the laser-altered wavefunction of the departing electron. In the second case, charge localization arises owing to laser-driven population transfer between different electronic states of the molecular ion. These results establish attosecond pump-probe strategies as a powerful tool for investigating the complex molecular dynamics that result from the coupling between electronic and nuclear motions beyond the usual Born-Oppenheimer approximation.

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Electron localization following attosecond molecular photoionization

A strong laser field may tunnel ionize a molecule from several orbitals simultaneously, forming an attosecond electron–hole wavepacket. Both temporal and spatial information on this wavepacket can be obtained through the coherent soft X-ray emission resulting from the laser-driven recollision of the liberated electron with the core. By characterizing the emission from aligned N 2 molecules, we demonstrate the attosecond contributions of the two highest occupied molecular orbitals. We determine conditions where they are disentangled in the real and imaginary parts of the emission dipole moment. This allows us to carry out a tomographic reconstruction of both orbitals with angstrom spatial resolution. Their coherent superposition provides experimental images of the attosecond wavepacket created in the ionization process. Our results open the prospect of imaging ultrafast intramolecular dynamics combining attosecond and angstrom resolutions.

/pdf/attosecond-imaging-of-molecular-electronic-wavepackets-tagfrbg1eb.pdf

Attosecond imaging of molecular electronic wavepackets

The generation of extremely short isolated attosecond pulses requires both a broad spectral bandwidth and control of the spectral phase. Rapid progress has been made in both aspects, leading to the generation of light pulses as short as 67 as in 2012, and broadband attosecond continua covering a wide range of extreme ultraviolet and soft X-ray wavelengths. Such pulses have been successfully applied in photoelectron and photoion spectroscopy and recently developed attosecond transient absorption spectroscopy to study electron dynamics in matter. In this Review, we discuss significant recent advances in the generation, characterization and applications of ultrabroadband, isolated attosecond pulses with spectral bandwidths comparable to the central frequency. These pulses can in principle be compressed to a single optical cycle. This review discusses significant recent advances in the generation, characterization and application of ultrabroadband isolated attosecond pulses with a spectral bandwidth comparable to the central frequency, which can in principle be compressed to a single optical cycle.

The generation, characterization and applications of broadband isolated attosecond pulses

Attosecond electron wavepackets are produced when an intense laser field ionizes an atom or a molecule1. When the laser field drives the wavepackets back to the parent ion, they interfere with the bound wavefunction, producing coherent subfemtosecond extreme-ultraviolet light bursts. When only a single return is possible2,3, an isolated attosecond pulse is generated. Here we demonstrate that by modulating the polarization of a carrier-envelope phase-stabilized short laser pulse4, we can finely control the electron-wavepacket dynamics. We use high-order harmonic generation to probe these dynamics. Under optimized conditions, we observe the signature of a single return of the electron wavepacket over a large range of energies. This temporally confines the extreme-ultraviolet emission to an isolated attosecond pulse with a broad and tunable bandwidth. Our approach is very general, and extends the bandwidth of attosecond isolated pulses in such a way that pulses of a few attoseconds seem achievable. Similar temporal resolution could also be achieved by directly using the broadband electron wavepacket. This opens up a new regime for time-resolved tomography of atomic or molecular wavefunctions5,6 and ultrafast dynamics.

/pdf/controlling-attosecond-electron-dynamics-by-phase-stabilized-20pg5twtuw.pdf

Controlling attosecond electron dynamics by phase-stabilized polarization gating

We suggest a high-order harmonic generation (HHG) model describing enhancement of the generation efficiency for the harmonic resonant with the transition between the ground and autoionizing state of the generating ion. The results of numerical and analytical calculations based on this model are in good quantitative agreement with the experiments showing HHG enhancement up to 2 orders of magnitude. Moreover, this model reproduces well the essential difference in HHG efficiency for different ions. We show that intense but relatively long attosecond pulses can be generated using the enhanced harmonics.

Role of autoionizing state in resonant high-order harmonic generation and attosecond pulse production.

We study XUV generation with several-cycle laser pulses of intensity up to 1015 W cm−2 using numerical solution of the 3D Schrodinger equation for a hydrogen atom. Ionization of the atom mainly takes place in a barrier-suppression regime for such driving intensities. We find that in this regime XUV yield stops growing with the laser intensity and then even essentially decreases. The calculated yield dependence on the laser intensity agrees well with predictions of our theory. The latter shows several factors that lead to the decrease of the XUV yield in the barrier-suppression regime. The calculated cut-off in the XUV spectrum is displaced to slightly lower energies than those predicted by the Ip + 3.17Up law. The change in the cut-off can be due to the non-zero initial velocity of the electron detached under the barrier-suppression ionization. We find that essential population of both the free wave packet returning to the origin and the ground state at the instant of the return is required for effective XUV generation. Rapid ground state depopulation leads to shortening of the attopulse train generated by the two-cycle laser pulse when laser intensity increases. In particular, we find that the cut-off XUV generated under essential barrier-suppression with sine-like laser pulse provides an isolated attopulse, while two attopulses are generated for lower laser intensity.

http://iopscience.iop.org/article/10.1088/0953-4075/39/3/011/pdf

XUV generation with several-cycle laser pulse in barrier-suppression regime

We present a quantum-mechanical theory of xuv generation by an elliptically polarized intense laser field. Our approach is valid when the Keldysh parameter $\ensuremath{\gamma}$ is about unity or less, and the driving ellipticity is less than $\sqrt{2}\ensuremath{\gamma}$. After the photoionization the motion of the electronic wave packet along the major axis of the driving field polarization ellipse is described quasiclassically, whereas the motion in the transverse direction is considered fully quantum mechanically; we also find the condition that allows the reduction of the motion description to a quantum orbit in the polarization plane of the laser field. We use the ionization rate calculated via numerical solution of the three-dimensional Schr\"odinger equation (TDSE), and take into account the Coulomb modification of the free electronic wave packet. The predictions of our theory for xuv emission agree well with numerical and experimental results. We study the high harmonic intensities and phases as functions of the driving intensity and ellipticity, and also the ellipticity and the rotation angle of the harmonic field polarization ellipse as functions of the driving ellipticity. The atomic response is decomposed into the contributions of different quantum paths. This allows finding a straightforward explanation for the observed dependencies.

V. V. Strelkov

Papers

Controlling attosecond electron dynamics by phase-stabilized polarization gating

Role of autoionizing state in resonant high-order harmonic generation and attosecond pulse production.

XUV generation with several-cycle laser pulse in barrier-suppression regime

Theory of high-order harmonic generation and attosecond pulse emission by a low-frequency elliptically polarized laser field

A new similarity measure for histogram comparison and its application in time series analysis