Andreas Kaldun

Lorentz meets Fano in spectral line shapes: a universal phase and its laser control.

A Phase for Fano In spectroscopy, samples placed between a steady light source and a detector are characterized based on the relative intensities of light absorbed at different frequencies. Temporal behavior—the relaxation of a photoexcited state—can be indirectly inferred from the absorption band shapes. The advent of ultrafast laser technology has enabled increasingly sophisticated measurements directly in the time domain. Ott et al. (p. 716; see the Perspective by Lin and Chu) present an analytical framework to account for asymmetric band shapes, termed Fano profiles, on the basis of a phase shift in the temporal dipole response. An analytical framework bolstered by attosecond spectroscopy conveys a clear understanding of asymmetric spectral line shapes. [Also see Perspective by Lin and Chu] Symmetric Lorentzian and asymmetric Fano line shapes are fundamental spectroscopic signatures that quantify the structural and dynamical properties of nuclei, atoms, molecules, and solids. This study introduces a universal temporal-phase formalism, mapping the Fano asymmetry parameter q to a phase ϕ of the time-dependent dipole response function. The formalism is confirmed experimentally by laser-transforming Fano absorption lines of autoionizing helium into Lorentzian lines after attosecond-pulsed excitation. We also demonstrate the inverse, the transformation of a naturally Lorentzian line into a Fano profile. A further application of this formalism uses quantum-phase control to amplify extreme-ultraviolet light resonantly interacting with He atoms. The quantum phase of excited states and its response to interactions can thus be extracted from line-shape analysis, with applications in many branches of spectroscopy.

Reconstruction and control of a time-dependent two-electron wave packet

The concerted motion of two or more bound electrons governs atomic and molecular non-equilibrium processes including chemical reactions, and hence there is much interest in developing a detailed understanding of such electron dynamics in the quantum regime. However, there is no exact solution for the quantum three-body problem, and as a result even the minimal system of two active electrons and a nucleus is analytically intractable. This makes experimental measurements of the dynamics of two bound and correlated electrons, as found in the helium atom, an attractive prospect. However, although the motion of single active electrons and holes has been observed with attosecond time resolution, comparable experiments on two-electron motion have so far remained out of reach. Here we show that a correlated two-electron wave packet can be reconstructed from a 1.2-femtosecond quantum beat among low-lying doubly excited states in helium. The beat appears in attosecond transient-absorption spectra measured with unprecedentedly high spectral resolution and in the presence of an intensity-tunable visible laser field. We tune the coupling between the two low-lying quantum states by adjusting the visible laser intensity, and use the Fano resonance as a phase-sensitive quantum interferometer to achieve coherent control of the two correlated electrons. Given the excellent agreement with large-scale quantum-mechanical calculations for the helium atom, we anticipate that multidimensional spectroscopy experiments of the type we report here will provide benchmark data for testing fundamental few-body quantum dynamics theory in more complex systems. They might also provide a route to the site-specific measurement and control of metastable electronic transition states that are at the heart of fundamental chemical reactions.

Fractional high-order harmonic combs and energy tuning by attosecond-precision split-spectrum pulse control

We experimentally control high-order harmonic generation by applying a versatile few-cycle pulse-shape control method: splitting up a single broadband continuous laser spectrum into two sections and applying sub-femtosecond relative time delays. For certain time delays, fractional high-harmonic combs (noninteger harmonics) are generated which we find to result from the controlled interference of two attosecond pulse trains. We also observe time-delay-dependent energy-tunability of the high-order harmonics for an asymmetrically split spectrum consisting of a strong and a weak component. The tuning mechanism is quantitatively understood by the controlled modulation of the instantaneous driver frequency at the peak of the shaped laser pulse.

Noisy Optical Pulses Enhance the Temporal Resolution of Pump-Probe Spectroscopy

Time-resolved measurements of quantum dynamics are based on the availability of controlled events that are shorter than the typical evolution time scale of the processes to be observed. Here we introduce the concept of noise-enhanced pump-probe spectroscopy, allowing the measurement of dynamics significantly shorter than the average pulse duration by exploiting randomly varying, partially coherent light fields consisting of bunched colored noise. These fields are shown to be superior by more than a factor of 10 to frequency-stabilized fields, with important implications for time-resolved experiments at x-ray free-electron lasers and, in general, for measurements at the frontiers of temporal resolution (e.g., attosecond spectroscopy). As an example application, the concept is used to explain the recent experimental observation of vibrational wave-packet motion in D(2)(+) on time scales shorter than the average pulse duration.

Two-dimensional spectral interpretation of time-dependent absorption near laser-coupled resonances

We demonstrate a two-dimensional time-domain spectroscopy method to extract amplitude and phase modifications of excited atomic states caused by the interaction with ultrashort laser pulses. The technique is based on Fourier analysis of the absorption spectrum of perturbed polarization decay. An analytical description of the method reveals how amplitude and phase information can be directly obtained from measurements. We apply the method experimentally to the helium atom, which is excited by attosecond-pulsed extreme ultraviolet light, to characterize laser-induced couplings of doubly excited states.

Time-resolved four-wave-mixing spectroscopy for inner-valence transitions

Noncollinear four-wave-mixing (FWM) techniques at near-infrared (NIR), visible, and ultraviolet frequencies have been widely used to map vibrational and electronic couplings, typically in complex molecules. However, correlations between spatially localized inner-valence transitions among different sites of a molecule in the extreme ultraviolet (XUV) spectral range have not been observed yet. As an experimental step toward this goal, we perform time-resolved FWM spectroscopy with femtosecond NIR and attosecond XUV pulses. The first two pulses (XUV-NIR) coincide in time and act as coherent excitation fields, while the third pulse (NIR) acts as a probe. As a first application, we show how coupling dynamics between odd- and even-parity, inner-valence excited states of neon can be revealed using a two-dimensional spectral representation. Experimentally obtained results are found to be in good agreement with ab initio time-dependent R-matrix calculations providing the full description of multielectron interactions, as well as few-level model simulations. Future applications of this method also include site-specific probing of electronic processes in molecules.

In situ characterization of few-cycle laser pulses in transient absorption spectroscopy

Attosecond transient absorption spectroscopy has thus far been lacking the capability to simultaneously characterize the intense laser pulses at work within a time-resolved quantum-dynamics experiment. However, precise knowledge of these pulses is key to extracting quantitative information in strong-field highly nonlinear light-matter interactions. Here, we introduce and experimentally demonstrate an ultrafast metrology tool based on the time-delay-dependent phase shift imprinted on a strong-field-driven resonance. Since we analyze the signature of the laser pulse interacting with the absorbing spectroscopy target, the laser pulse duration and intensity are determined in situ. As we also show, this approach allows for the quantification of time-dependent bound-state dynamics in one and the same experiment. In the future, such experimental data will facilitate more precise tests of strong-field dynamics theories.

Spectral narrowing of x-ray pulses for precision spectroscopy with nuclear resonances

Spectral narrowing of x-rays Modern photon factories typically provide x-ray pulses that are orders of magnitude broader in frequency space than the corresponding atomic or nuclear resonances to be probed. For many spectroscopic applications, however, narrower x-ray light sources are desired. By using precise mechanical displacements of a reference absorber to simulate the effect of an x-ray control field, Heeg et al. show that they can spectrally narrow input x-ray pulses. The conversion of off-resonant photons into resonant ones results in increased pulse brilliance at the desired resonant frequency, thereby providing a sharp x-ray probe for precision spectroscopy. Science, this issue p. 375 A method is introduced for the spectral narrowing of x-ray pulses. Spectroscopy of nuclear resonances offers a wide range of applications due to the remarkable energy resolution afforded by their narrow linewidths. However, progress toward higher resolution is inhibited at modern x-ray sources because they deliver only a tiny fraction of the photons on resonance, with the remainder contributing to an off-resonant background. We devised an experimental setup that uses the fast mechanical motion of a resonant target to manipulate the spectrum of a given x-ray pulse and to redistribute off-resonant spectral intensity onto the resonance. As a consequence, the resonant pulse brilliance is increased while the off-resonant background is reduced. Because our method is compatible with existing and upcoming pulsed x-ray sources, we anticipate that this approach will find applications that require ultranarrow x-ray resonances.

Watching the emergence of a Fano resonance in doubly excited helium

We report on the experimental observation of the buildup of the 2s2p Fano resonance in helium in the time domain, which has been under theoretical investigation for more than a decade. The emergence of the absorption line is temporally resolved by interrupting the natural decay of the excited state via saturated strong-field ionization at a variable time delay. We compare the experimental data with full ab-initio simulations to validate the time-gating by strong-field ionization and thereby confirm the recently developed theory for the formation of Fano line-profiles.

Fano Resonances in the Time Domain

The Fano phase formalism enables measurement and control of phase and amplitude of an emitting dipole. Here, we use this formalism to measure and understand the dynamics of bound atomic states in strong laser fields.