Mette B. Gaarde

Macroscopic aspects of attosecond pulse generation

Attosecond pulses are generated by a macroscopic number of ionizing atoms interacting with a focused laser pulse, via the process of high harmonic generation. The physics of their generation consists of an interplay between the microscopic laser–atom interaction and macroscopic effects due to ionization and phase matching in the nonlinear medium. In this review, we focus on a complete understanding of the way in which attosecond pulses arrive at a target where they can be characterized and used in an experiment. We discuss a number of results from calculations of attosecond pulse generation obtained by simultaneous solution of the time-dependent Schrodinger equation and the Maxwell wave equation. These results, which allow for a clean separation of microscopic and macroscopic factors, illustrate how macroscopic effects are used to select attosecond pulses from the radiation that is emitted by atoms interacting with a strong laser field.

Vacuum-ultraviolet frequency combs from below-threshold harmonics

Frequency combs have revolutionized frequency metrology. High-harmonic generation in atoms has led to fast sources of short-wavelength photons. Combining these two technologies enables the transfer of frequency combs to the vacuum-ultraviolet with potential applications in spectroscopy.

Solid-state harmonics beyond the atomic limit

Strong-field laser excitation of solids can produce extremely nonlinear electronic and optical behaviour. As recently demonstrated, this includes the generation of high harmonics extending into the vacuum-ultraviolet and extreme-ultraviolet regions of the electromagnetic spectrum. High harmonic generation is shown to occur fundamentally differently in solids and in dilute atomic gases. How the microscopic mechanisms in the solid and the gas differ remains a topic of intense debate. Here we report a direct comparison of high harmonic generation in the solid and gas phases of argon and krypton. Owing to the weak van der Waals interaction, rare (noble)-gas solids are a near-ideal medium in which to study the role of high density and periodicity in the generation process. We find that the high harmonic generation spectra from the rare-gas solids exhibit multiple plateaus extending well beyond the atomic limit of the corresponding gas-phase harmonics measured under similar conditions. The appearance of multiple plateaus indicates strong interband couplings involving multiple single-particle bands. We also compare the dependence of the solid and gas harmonic yield on laser ellipticity and find that they are similar, suggesting the importance of electron–hole recollision in these solids. This implies that gas-phase methods such as polarization gating for attosecond pulse generation and orbital tomography could be realized in solids.

Frequency chirp of harmonic and attosecond pulses

We study the phase of the atomic polarization in the process of high-order harmonic generation. Its dependence on the laser intensity and the harmonic order induce a frequency variation in time (chirp) respectively of the harmonic pulses and attosecond pulses. We review the recent experimental results on the temporal characterization of the harmonic emission and show that measurements performed using very different techniques (like XFROG and RABITT), probing the phase in different parameter spaces, can be connected through the mixed phase derivatives, demonstrating the common underlying physics.

Single attosecond pulses from high harmonics driven by self-compressed filaments

We show that isolated subfemtosecond, extreme ultraviolet (XUV) pulses can be generated via harmonic generation in argon by few-cycle infrared pulses formed through filamentation-induced self-compression in neon. Our calculations show that the time structure of the XUV pulses depends sensitively on both the amplitude and the phase modulation that are induced in the driving pulse during the self-compression process.

Generating single attosecond pulses via spatial filtering

The first observation of isolated attosecond pulses by Hentschel [Nature 414, 509 (2001)] resulted from an experiment that left the exact mechanism of their generation unresolved. A complete simulation of the experiment reveals the reason for its success: single pulses were efficiently isolated from two or more generated pulses by spatial filtering in the far field. Our explanation suggests a new, simple paradigm for the production of isolated attosecond bursts. We show that this method can be used, in conjunction with carrier-envelope phase stabilization, to select single attosecond pulses by use of 10 fs driving pulses.

High-order harmonic generation directly from a filament

The synthesis of isolated attosecond pulses (IAPs) in the extreme ultraviolet (XUV) spectral region has opened up the shortest time scales for time- resolved studies. It relies on the generation of high-order harmonics (HHG) from high-power few-cycle infrared (IR) laser pulses. Here we explore experimentally a new and simple route to IAP generation directly from 35fs IR pulses that undergo filamentation in argon. Spectral broadening, self-shortening of the IR pulse and HHG are realized in a single stage, reducing the cost and experimental effort for easier spreading of attosecond sources. We observe continuous XUV spectra supporting IAPs, emerging directly from the filament via a truncating pinhole to vacuum. The extremely short absorption length of the XUV radiation makes it a highly local probe for studying the elusive filamentation dynamics and in particular provides an experimental diagnostic of short-lived spikes in

Attosecond transient absorption probing of electronic superpositions of bound states in neon. Detection of quantum beats

Electronic wavepackets composed of multiple bound excited states of atomic neon lying between 19.6 and 21.5 eV are launched using an isolated attosecond pulse. Individual quantum beats of the wavepacket are detected by perturbing the induced polarization of the medium with a time-delayed few-femtosecond near-infrared (NIR) pulse via coupling the individual states to multiple neighboring levels. All of the initially excited states are monitored simultaneously in the attosecond transient absorption spectrum, revealing Lorentzian to Fano lineshape spectral changes as well as quantum beats. The most prominent beating of the several that were observed was in the spin–orbit split 3d absorption features, which has a 40 femtosecond period that corresponds to the spin–orbit splitting of 0.1 eV. The few-level models and multilevel calculations confirm that the observed magnitude of oscillation depends strongly on the spectral bandwidth and tuning of the NIR pulse and on the location of possible coupling states.

Quantum interference in attosecond transient absorption of laser-dressed helium atoms

We calculate the transient absorption of an isolated attosecond pulse by helium atoms subject to a delayed infrared (\ir) laser pulse. With the central frequency of the broad attosecond spectrum near the ionization threshold, the absorption spectrum is strongly modulated at the sub-\ir-cycle level. Given that the absorption spectrum results from a time-integrated measurement, we investigate the extent to which the delay-dependence of the absorption yields information about the attosecond dynamics of the atom-field energy exchange. We find two configurations in which this is possible. The first involves multi photon transitions between bound states that result in interference between different excitation pathways. The other involves the modification of the bound state absorption lines by the IR field, which we find can result in a sub-cycle time dependence only when ionization limits the duration of the strong field interaction.

Multilevel perspective on high-order harmonic generation in solids

We investigate high-order harmonic generation in a solid, modeled as a multilevel system dressed by a strong infrared laser field. We show that the cutoff energies and the relative strengths of the multiple plateaus that emerge in the harmonic spectrum can be understood both qualitatively and quantitatively by considering a combination of adiabatic and diabatic processes driven by the strong field. Such a model was recently used to interpret the multiple plateaus exhibited in harmonic spectra generated by solid argon and krypton [G. Ndabashimiye et al., Nature 534, 520 (2016)]. We also show that when the multilevel system originates from the Bloch state at the