Intense ultrashort light pulses comprising merely a few wave cycles became routinely available by the turn of the millennium. The technologies underlying their production and measurement as well as relevant theoretical modeling have been reviewed in the pages of Reviews of Modern Physics (Brabec and Krausz, 2000). Since then, measurement and control of the subcycle field evolution of few-cycle light have opened the door to a radically new approach to exploring and controlling processes of the microcosm. The hyperfast-varying electric field of visible light permitted manipulation and tracking of the atomic-scale motion of electrons. Striking implications include controlled generation and measurement of single attosecond pulses of extreme ultraviolet light as well as trains of them, and real-time observation of atomic-scale electron dynamics. The tools and techniques for steering and tracing electronic motion in atoms, molecules, and nanostructures are now becoming available, marking the birth of attosecond physics. In this article these advances are reviewed and some of the expected implications are addressed. 

Attosecond physics

The rise time of intense radiation determines the maximum field strength atoms can be exposed to before their polarizability dramatically drops due to the detachment of an outer electron. Recent progress in ultrafast optics has allowed the generation of ultraintense light pulses comprising merely a few field oscillation cycles. The arising intensity gradient allows electrons to survive in their bound atomic state up to external field strengths many times higher than the binding Coulomb field and gives rise to ionization rates comparable to the light frequency, resulting in a significant extension of the frontiers of nonlinear optics and (nonrelativistic) high-field physics. Implications include the generation of coherent harmonic radiation up to kiloelectronvolt photon energies and control of the atomic dipole moment on a subfemtosecond $(1{\mathrm{f}\mathrm{s}=10}^{\mathrm{\ensuremath{-}}15}\mathrm{}\mathrm{s})$ time scale. This review presents the landmarks of the 30-odd-year evolution of ultrashort-pulse laser physics and technology culminating in the generation of intense few-cycle light pulses and discusses the impact of these pulses on high-field physics. Particular emphasis is placed on high-order harmonic emission and single subfemtosecond extreme ultraviolet/x-ray pulse generation. These as well as other strong-field processes are governed directly by the electric-field evolution, and hence their full control requires access to the (absolute) phase of the light carrier. We shall discuss routes to its determination and control, which will, for the first time, allow access to the electromagnetic fields in light waves and control of high-field interactions with never-before-achieved precision.

Intense few-cycle laser fields: Frontiers of nonlinear optics

Single-electron wavefunctions, or orbitals, are the mathematical constructs used to describe the multi-electron wavefunction of molecules. Because the highest-lying orbitals are responsible for chemical properties, they are of particular interest. To observe these orbitals change as bonds are formed and broken is to observe the essence of chemistry. Yet single orbitals are difficult to observe experimentally, and until now, this has been impossible on the timescale of chemical reactions. Here we demonstrate that the full three-dimensional structure of a single orbital can be imaged by a seemingly unlikely technique, using high harmonics generated from intense femtosecond laser pulses focused on aligned molecules. Applying this approach to a series of molecular alignments, we accomplish a tomographic reconstruction of the highest occupied molecular orbital of N2. The method also allows us to follow the attosecond dynamics of an electron wave packet.

Tomographic imaging of molecular orbitals

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

The amplitude and frequency of laser light can be routinely measured and controlled on a femtosecond (10(-15) s) timescale. However, in pulses comprising just a few wave cycles, the amplitude envelope and carrier frequency are not sufficient to characterize and control laser radiation, because evolution of the light field is also influenced by a shift of the carrier wave with respect to the pulse peak. This so-called carrier-envelope phase has been predicted and observed to affect strong-field phenomena, but random shot-to-shot shifts have prevented the reproducible guiding of atomic processes using the electric field of light. Here we report the generation of intense, few-cycle laser pulses with a stable carrier envelope phase that permit the triggering and steering of microscopic motion with an ultimate precision limited only by quantum mechanical uncertainty. Using these reproducible light waveforms, we create light-induced atomic currents in ionized matter; the motion of the electronic wave packets can be controlled on timescales shorter than 250 attoseconds (250 x 10(-18) s). This enables us to control the attosecond temporal structure of coherent soft X-ray emission produced by the atomic currents--these X-ray photons provide a sensitive and intuitive tool for determining the carrier-envelope phase.

Attosecond control of electronic processes by intense light fields

Subfemtosecond light pulses can be obtained by superposing several high harmonics of an intense laser pulse. Provided that the harmonics are emitted simultaneously, increasing their number should result in shorter pulses. However, we found that the high harmonics were not synchronized on an attosecond time scale, thus setting a lower limit to the achievable x-ray pulse duration. We showed that the synchronization could be improved considerably by controlling the underlying ultrafast electron dynamics, to provide pulses of 130 attoseconds in duration. We discuss the possibility of achieving even shorter pulses, which would allow us to track fast electron processes in matter.

https://science.sciencemag.org/content/sci/302/5650/1540.full.pdf

Attosecond Synchronization of High-Harmonic Soft X-rays

We consider harmonic generation by atoms exposed to an intense laser pulse of a few femtoseconds. Our results, obtained by solving numerically the corresponding 3-dimensional time-dependent Schrodinger equation, demonstrate that the harmonic spectra are extremely sensitive to the phase of the laser field. Depend- ing on this phase, the harmonics in the cutoff are resolved or not resolved. The position of the cutoff itself varies with the phase and the so-called “plateau” region exhibits two well-distinct parts: a series of well-defined har- monics followed in the high-frequency region by a series of broad peaks which are not separated any more by twice the laser field frequency. These results are explained in terms of both quantum and classical dynamics. We also show that this phase sensitivity may be exploited in order to probe the phase of the electric field of an ultrashort laser pulse in a single shot experiment. Our discussion about this new method of diagnosis takes into account propagation effects.

Phase sensitivity of harmonic emission with ultrashort laser pulses

Plateau high harmonics are shown to be chirped. The experimental values of the chirp, in good agreement with purely classical kinematics or strong field approximation quantum theory are positive and inversely proportional to intensity. The various steps for the optimization of the attosecond pulse train are discussed.

High-harmonics chirp and optimization of attosecond pulse trains

We demonstrate that the main features of high harmonic generation by ultrashort laser pulses can be explained in terms of the intensity dependent phase of the atomic polarization. Focusing conditions and chirped driving fields may be used to control the harmonic spectrum, while temporal compression provides a unique way to tailor the time profile.

Temporal and spectral tailoring of high-order harmonics

In this paper we present some results of a high-harmonic generation experiment in argon, performed with a Ti sapphire laser (787 nm, 140 fs) and a spatially shaped focus (flat top). The range of intensities is 3-100 TW cm(-2) The intensity dependence of the harmonic signal shows an interesting behaviour of the 13th harmonic, namely an initial suppression followed by a strong enhancement at similar or equal to 85 TW cm(-2), which exceeds the magnitude of the 11th harmonic. This behaviour is a consequence of a resonant atomic process. Numerical calculations were also performed. They partly reproduced the experiment.

Resonance-enhanced high-harmonic generation

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