Philipp Raith

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.

High Harmonic Generation Via Continuum Wave-Packet Interference

High-order harmonic generation (HHG) is investigated theoretically in the over-the-barrier ionization regime revealing the strong signature of interference between two separately ionized and separately propagating free wave packets of a single electron. The interference leads to the emission of coherent light at a photon energy corresponding to the kinetic-energy difference of the two recolliding electron quantum paths, thus complementary to the well-known classical three-step picture of HHG. As will be shown by time-frequency analysis of the emitted radiation, the process entirely dominates the coherent HHG emission after the atomic ground state has been depleted by a strong field. Moreover, it can be isolated from the continuum-bound harmonics via phase matching.

Attosecond twin-pulse control by generalized kinetic heterodyne mixing

Attosecond double-pulse (twin-pulse) production in high-order harmonic generation is manipulated by a combination of two-color and carrier-envelope phase-control methods. As we show in numerical simulations, both relative amplitude and phase of the double pulse can be independently set by making use of multidimensional parameter control. Two technical implementation routes are discussed: kinetic heterodyning using second-harmonic generation and split-spectrum phase-step control.

Sub-cycle strong-field interferometry.

A nonlinear interferometry scheme is described theoretically to induce and resolve electron wavefunction beating on time scales shorter than the optical cycle of the time-delayed pump and probe pulses. By employing two moderately intense few-cycle laser fields with a stable carrier-envelope phase, a large range of the entire electronic level structure of a quantum system can be retrieved. In contrast to single-photon excitation schemes, the retrieved electronic states include levels that are both dipole- and non-dipole-accessible from the ground electronic state. The results show that strong-field interferometry can reveal both high-resolution and broad-band spectral information at the same time with important consequences for quantum-beat spectroscopy on attosecond time scales.

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.

Temporal resolution in pump–probe experiments enhanced by noisy pulses

We show that statistically varying light fields as they are provided by Free-Electron Laser (FEL) sources can be used to enhance the temporal resolution in pump-probe experiments. Dynamics on time scales more than a factor of ten shorter than the average pulse duration can be measured. The mechanism is based on correlated noise in pump and probe pulses and is demonstrated for the example of wave-packet dynamics in D2 molecules as investigated in a recent experiment.

Carrier-envelope phase- and spectral control of fractional high-harmonic combs

We experimentally and numerically control high-harmonic generation (HHG) by time delaying variable segments of a few-cycle driving laser spectrum. In this configuration combs of fractional high harmonics can be produced by interference of two temporally spaced attosecond pulse trains. We explain the observed beating of the high-harmonic intensity with the time delay and study the influence of the spectral segmentation on the high harmonics. By the implementation of additional carrier-envelope phase (CEP) control, we extend the control configuration and demonstrate independent multi-parameter controllability of HHG purely enabled by the CEP and the time delay between two spectral segments. We present how specific properties of the fractional harmonics can be optimized. Analyzing the measured fractional harmonic combs by a spectral interferometry method, we find that the relative phase between the two contributing attosecond pulse trains can be freely set by the CEP of the driving laser field. We also discu...