Molecular interferometer to decode attosecond electron-nuclear dynamics

Strong Laser Field-Driven Coupled Electron-Nuclear Dynamics: Quantum vs Classical Description

We have performed a coupled electron-nuclear dynamics study of H2+ molecular ions under the influence of an intense few-cycle 4.5 fs laser pulse with an intensity of 4 × 1014 W/cm2 and a central wavelength of 750 nm. Both quantum and classical dynamical methods are employed in the exact similar initial conditions with the aim of head-to-head comparison of two methodologies. A competition between ionization and dissociation channel is explained under the framework of quantum and classical dynamics. The origin of the electron localization phenomena is elucidated by observing the molecular and electronic wave packet evolution pattern. By probing with different carrier envelope phase (CEP) values of the ultrashort pulse, the possibility of electron localization on either of the two nuclei is investigated. The effects of initial vibrational states on final dissociation and ionization probabilities for several CEP values are studied in detail. Finally, asymmetries in the dissociation probabilities are calculated and mutually compared for both quantum and classical dynamical methodologies, whereas Franck-Condon averaging over the initial vibrational states is carried out in order to mimic the existing experimental conditions.

Attosecond spectroscopy for the investigation of ultrafast dynamics in atomic, molecular and solid-state physics

Since the first demonstration of the generation of attosecond pulses (1 as = 10^-18s) in the extreme-ultraviolet spectral region, several measurement techniques have been introduced, at the beginning for the temporal characterization of the pulses, and immediately after for the investigation of electronic and nuclear ultrafast dynamics in atoms, molecules and solids with unprecedented temporal resolution. The attosecond spectroscopic tools established in the last two decades, together with the development of sophisticated theoretical methods for the interpretation of the experimental outcomes, allowed to unravel and investigate physical processes never observed before, such as the delay in photoemission from atoms and solids, the motion of electrons in molecules after prompt ionization which precede any notable nuclear motion, the temporal evolution of the tunneling process in dielectrics, and many others. This review focused on applications of attosecond techniques to the investigation of ultrafast processes in atoms, molecules and solids. Thanks to the introduction and ongoing developments of new spectroscopic techniques, the attosecond science is rapidly moving towards the investigation, understanding and control of coupled electron-nuclear dynamics in increasingly complex systems, with ever more accurate and complete investigation techniques. Here we will review the most common techniques presenting the latest results in atoms, molecules and solids.

Molecular fragmentation as a way to reveal early electron dynamics induced by attosecond pulses

We present a theoretical study of the electron and nuclear dynamics that would arise in an attosecond two-color XUV-pump/XUV-probe experiment in glycine. In this scheme, the broadband pump pulse suddenly ionizes the molecule and creates an electronic wave packet that subsequently evolves under the influence of the nuclear motion until it is finally probed by the second XUV pulse. To describe the different steps of such an experiment, we have combined a multi-reference static-exchange scattering method with a trajectory surface hopping approach. We show that by changing the central frequency of the pump pulse, i.e., by engineering the initial electronic wave packet with the pump pulse, one can drive the cation dynamics into a specific fragmentation pathway. Reminiscence of this early electron dynamics can be observed in specific fragmentation channels (not all of them) as a function of the pump-probe delay and in time-resolved photoelectron spectra at specific photoelectron energies. The optimum conditions to visualize the initial electronic coherence in photoelectron and photo-ion spectra depend very much on the characteristics of the pump pulse as well as on the electronic structure of the molecule under study.

Imaging of electron transition and bond breaking in the photodissociation of H2+ via ultrafast X-ray photoelectron diffraction

We theoretically investigate the photodissociation dynamics of H2+ using the methodology of ultrafast X-ray photoelectron diffraction (UXPD). We use a femtosecond infrared pulse to prompt a coherent excitation from the molecular vibrational state (v = 9) of the electronic ground state (1sσ_g) and then adopt another time-delayed attosecond X-ray pulse to probe the dynamical properties. We have calculated photoionization momentum distributions by solving the non-Born-Oppenheimer time-dependent Schrödinger equation (TDSE). We unambiguously identify the phenomena associated with the g - u symmetry breakdown in the time-resolved photoelectron diffraction spectra. Using the two-center interference model, we can determine the variation in nuclear spacing with high accuracy. In addition, we use a strong field approximation (SFA) model to interpret the UXPD profile, and the SFA simulations can reproduce the TDSE results in a quantitative way.

Quantum state holography to reconstruct the molecular wave packet using an attosecond XUV-XUV pump-probe technique

An attosecond molecular interferometer is proposed by using a XUV-XUV pump-probe scheme. The interferograms resulting in the photoelectron distributions enable the full reconstruction of the molecular wave packet associated to excited states using a quantum state holographic approach that, to our knowledge, has only been proposed for simple atomic targets combining attosecond XUV pulses with IR light. In contrast with existing works, we investigate schemes where one- and two-photon absorption paths contribute to ionize the hydrogen molecule and show that it is possible to retrieve the excitation dynamics even when imprinted in a minority channel. Furthermore, we provide a systematic analysis of the time-frequency maps that reveal the distinct, but tightly coupled, motion of electrons and nuclei.

Α 10-gigawatt attosecond source for non-linear XUV optics and XUV-pump-XUV-probe studies

The quantum mechanical motion of electrons and nuclei in systems spatially confined to the molecular dimensions occurs on the sub-femtosecond to the femtosecond timescales respectively. Consequently, the study of ultrafast electronic and, in specific cases, nuclear dynamics requires the availability of light pulses with attosecond (asec) duration and of sufficient intensity to induce two-photon processes, essential for probing the intrinsic system dynamics. The majority of atoms, molecules and solids absorb in the extreme-ultraviolet (XUV) spectral region, in which the synthesis of the required attosecond pulses is feasible. Therefore, the XUV spectral region optimally serves the study of such ultrafast phenomena. Here, we present a detailed review of the first 10-GW class XUV attosecond source based on laser driven high harmonic generation in rare gases. The pulse energy of this source largely exceeds other laser driven attosecond sources and is comparable to the pulse energy of femtosecond Free-Electron-Laser (FEL) XUV sources. The measured pulse duration in the attosecond pulse train is 650 ± 80 asec. The uniqueness of the combined high intensity and short pulse duration of the source is evidenced in non-linear XUV-optics experiments. It further advances the implementation of XUV-pump-XUV-probe experiments and enables the investigation of strong field effects in the XUV spectral region.

Ultrafast X-ray photoelectron diffraction in triatomic molecules by circularly polarized attosecond light pulses

We theoretically study ultrafast photoelectron diffraction in triatomic molecules with cyclic geometry by ultrafast circular soft X-ray attosecond pulses.

High-order above-threshold dissociation of molecules

Above-threshold ionization of atoms in strong laser fields is extensively studied for its overwhelming importance and universality. However, its counterpart, above-threshold dissociation of molecules in strong laser fields, is hard to be observed, although it has been predicted for decades. In this paper, by measuring the momenta of photoelectron and dissociative fragments coincidently, we successfully obtained distinct nuclear energy peaks of the high-order above-threshold dissociation, which must appear simultaneously with the above-threshold ionization. The coexistence of high-order above-threshold dissociation and high-order above-threshold ionization in molecular dissociative ionization offers a perspective to disentangle the complex electron–nuclear correlation in molecules and to image the molecular orbitals, and so on.

Electrons bound to atoms or molecules can simultaneously absorb multiple photons via the above-threshold ionization featured with discrete peaks in the photoelectron spectrum on account of the quantized nature of the light energy. Analogously, the above-threshold dissociation of molecules has been proposed to address the multiple-photon energy deposition in the nuclei of molecules. In this case, nuclear energy spectra consisting of photon-energy spaced peaks exceeding the binding energy of the molecular bond are predicted. Although the observation of such phenomena is difficult, this scenario is nevertheless logical and is based on the fundamental laws. Here, we report conclusive experimental observation of high-order above-threshold dissociation of H₂ in strong laser fields where the tunneling-ionized electron transfers the absorbed multiphoton energy, which is above the ionization threshold to the nuclei via the field-driven inelastic rescattering. Our results provide an unambiguous evidence that the electron and nuclei of a molecule as a whole absorb multiple photons, and thus above-threshold ionization and above-threshold dissociation must appear simultaneously, which is the cornerstone of the nowadays strong-field molecular physics.

Application of the complex Kohn variational method to attosecond spectroscopy

The complex Kohn variational method is extended to compute light-driven electronic transitions between continuum wave functions in atomic and molecular systems. This development enables the study of multiphoton processes in the perturbative regime for arbitrary light polarization. As a proof of principle, we apply the method to compute the photoelectron spectrum arising from the pump-probe two-photon ionization of helium induced by a sequence of extreme ultraviolet and infrared light pulses. We compare several two-photon ionization pump-probe spectra, resonant with the (2s2p) 1P 1 o Feshbach resonance, with independent simulations based on the atomic B-spline close-coupling STOCK code, and find good agreement between the two approaches. This finite-pulse perturbative approach is a step towards the ab initio study of weak-field attosecond processes in polyelectronic molecules.

Sub-10-fs control of dissociation pathways in the hydrogen molecular ion with a few-pulse attosecond pulse train

The control of the electronic states of a hydrogen molecular ion by photoexcitation is considerably difficult because it requires multiple sub-10 fs light pulses in the extreme ultraviolet (XUV) wavelength region with a sufficiently high intensity. Here, we demonstrate the control of the dissociation pathway originating from the 2pσu electronic state against that originating from the 2pπu electronic state in a hydrogen molecular ion by using a pair of attosecond pulse trains in the XUV wavelength region with a train-envelope duration of ∼4 fs. The switching time from the peak to the valley in the oscillation caused by the vibrational wavepacket motion in the 1sσg ground electronic state is only 8 fs. This result can be classified as the fastest control, to the best of our knowledge, of a molecular reaction in the simplest molecule on the basis of the XUV-pump and XUV-probe scheme.

Weak-field laser phase modulation coherent control of asymptotic photofragment distributions

Coherent control of the asymptotic photofragment state-resolved distributions by means of laser phase modulation in the weak-field limit is demonstrated computationally for a polyatomic molecule. The control scheme proposed applies a pump laser field consisting of two pulses delayed in time. Phase modulation of the spectral bandwidth profile of the laser field is achieved by varying the time delay between the pulses. The underlying equations show that such a phase modulation is effective in order to produce control effects on the asymptotic, long-time limit photofragment distributions only when the bandwidths of the two pulses overlap in a frequency range. The frequency overlap of the pulses gives rise to an interference term which is responsible for the modulation of the spectral profile shape. The magnitude of the range of spectral overlap between the pulses becomes an additional control parameter. The control scheme is illustrated computationally for the asymptotic photofragment state distributions produced from different scenarios of the Ne-Br2 predissociation. An experimental application of the control scheme is found to be straightforward.

Communication: Control of the fragment state distributions produced upon decay of an isolated resonance state

Control of the fragment state distributions produced upon decay of a resonance state is achieved by using a weak laser field consisting of two pulses with a varying time delay between them. It is shown that specific product fragment states can be significantly favored or quenched. The efficiency and flexibility of the control method are found to increase with increasing resonance width. The control scheme is completely independent of the specific system to which it is applied, which makes its applicability universal.

Generation of Phase-Locked Pulses from a Seeded Free-Electron Laser

In a coherent control experiment, light pulses are used to guide the real-time evolution of a quantum system. This requires the coherence and the control of the pulses' electric-field carrier waves. In this work, we use frequency-domain interferometry to demonstrate the mutual coherence of time-delayed pulses generated by an extreme ultraviolet seeded free-electron laser. Furthermore, we use the driving seed laser to lock and precisely control the relative phase between the two free-electron laser pulses. This new capability opens the way to a multitude of coherent control experiments, which will take advantage of the high intensity, short wavelength, and short duration of the pulses generated by seeded free-electron lasers.

Decoherence, control and attosecond probing of XUV-induced charge migration in biomolecules. A theoretical outlook

The sudden ionization of a molecule by an attosecond pulse is followed by charge redistribution on a time scale from a few femtoseconds down to hundreds of attoseconds. This ultrafast redistribution is the result of the coherent superposition of electronic continua associated with the ionization thresholds that are reached by the broadband attosecond pulse. Thus, a correct theoretical description of the time evolution of the ensuing wave packet requires the knowledge of the actual ionization amplitudes associated with all open ionization channels, a real challenge for large and medium-size molecules. Recently, the first calculation of this kind has come to light, allowing for interpretation of ultrafast electron dynamics observed in attosecond pump–probe experiments performed on the amino acid phenylalanine [Calegari et al., Science 2014, 346, 336]. However, as in most previous theoretical works, the interpretation was based on various simplifying assumptions, namely, the ionized electron was not included in the description of the cation dynamics, the nuclei were fixed at their initial position during the hole migration process, and the effect of the IR probe pulse was ignored. Here we go a step further and discuss the consequences of including these effects in the photoionization of the glycine molecule. We show that (i) the ionized electron does not affect hole dynamics beyond the first femtosecond, and (ii) nuclear dynamics has only a significant effect after approximately 8 fs, but does not destroy the coherent motion of the electronic wave packet during at least few additional tens of fs. As a first step towards understanding the role of the probe pulse, we have considered an XUV probe pulse, instead of a strong IR one, and show that such an XUV probe does not introduce significant distortions in the pump-induced dynamics, suggesting that pump–probe strategies are suitable for imaging and manipulating charge migration in complex molecules. Furthermore, we show that hole dynamics can be changed by shaping the attosecond pump pulse, thus opening the door to the control of charge dynamics in biomolecules.

Quantum interference control of an isolated resonance lifetime in the weak-field limit

Resonance states play an important role in a large variety of physical and chemical processes. Thus, controlling the resonance behavior, and particularly a key property like the resonance lifetime, opens up the possibility of controlling those resonance mediated processes. While such a resonance control is possible by applying strong-field approaches, the development of flexible weak-field control schemes that do not alter significantly the system dynamics still remains a challenge. In this work, one such control scheme within the weak-field regime is proposed for the first time in order to modify the lifetime of an isolated resonance state. The basis of the scheme suggested is quantum interference between two pathways induced by laser fields, that pump wave packet amplitude to the target resonance under control. The simulations reported here show that the scheme allows for both enhancement and quenching of the resonance survival lifetime, being particularly flexible to achieve large lifetime enhancements. Control effects on the resonance lifetime take place only while the pulse is operating. In addition, the conditions required to generate the two interfering quantum pathways are found to be rather easy to meet for general systems, which makes the experimental implementation straightforward and implies the wide applicability of the control scheme.