High-harmonic probing of electronic coherence in dynamically aligned molecules

Toward Complete All-Optical Intensity Modulation of High-Harmonic Generation from Solids

Optical modulation of high-harmonics generation in solids enables the detection of material properties, such as the band structure, and promising new applications, such as super-resolution imaging in semiconductors. Various recent studies have shown optical modulation of high-harmonics generation in solids, in particular, suppression of high-harmonics generation has been observed by synchronized or delayed multipulse sequences. Here we provide an overview of the underlying mechanisms attributed to this suppression and provide a perspective on the challenges and opportunities regarding these mechanisms. All-optical control of high-harmonic generation allows for femtosecond, and in the future possibly subfemtosecond, switching, which has numerous possible applications: These range from super-resolution microscopy to nanoscale controlled chemistry and highly tunable nonlinear light sources.

Ultrafast X-ray Diffraction Probe of Coherent Spin-State Dynamics in Molecules

We propose an approach to probe coherent spin-state dynamics of molecules using circularly polarized hard X-ray pulses. For the dynamically aligned nitric oxide molecules in a coherent superposition spin-orbit coupled electronic state that can be prepared through stimulated Raman scattering, we demonstrate the capability of ultrafast X-ray diffraction to not only reveal the quantum beating of the coherent spin-state wave packet but also image the spatial spin density of the molecule. With a circularly polarized ultrafast X-ray diffraction signal, we show that the electronic density matrix can be retrieved. The spatiotemporal resolving power of ultrafast X-ray diffraction paves the way for tracking transient spatial wave function in molecular dynamics involving the spin degree of freedom.

High-harmonic spectroscopy of impulsively aligned 1,3-cyclohexadiene: Signatures of attosecond charge migration

High-harmonic spectroscopy is an all-optical technique with inherent attosecond temporal resolution that has been successfully employed to reconstruct charge migration, electron-tunneling dynamics, and conical-intersection dynamics. Here, we demonstrate the extension of two key components of high-harmonic spectroscopy, i.e., impulsive alignment and measurements with multiple driving wavelengths to 1,3-cyclohexadiene and benzene. In the case of 1,3-cyclohexadiene, we find that the temporal sequence of maximal and minimal emitted high-harmonic intensities as a function of the delay between the alignment and probe pulses inverts between 25 and 30 eV and again between 35 and 40 eV when an 800-nm driver is used, but no inversions are observed with a 1420-nm driver. This observation is explained by the wavelength-dependent interference of emission from multiple molecular orbitals (HOMO to HOMO-3), as demonstrated by calculations based on the weak-field asymptotic theory and accurate photorecombination matrix elements. These results indicate that attosecond charge migration takes place in the 1,3-cyclohexadiene cation and can potentially be reconstructed with the help of additional measurements. Our experiments also demonstrate a pathway toward studying photochemical reactions in the molecular frame of 1,3-cyclohexadiene.

Transient High-Harmonic Spectroscopy in an Inorganic-Organic Lead Halide Perovskite

High-harmonic generation is the frequency upconversion of an intense femtosecond infrared laser in a material. In condensed-phase high-harmonic generation, laser-driven currents of coherently excited charge carriers map the electronic structure onto the emitted light. This promises a thus far scarcely explored potential of condensed-phase time-resolved high-harmonic spectroscopy for probing carrier dynamics. Here, we realize this potential and use time-resolved solid-state high-harmonic spectroscopy from a laser-excited methylammonium lead bromide (MAPbBr3) thin film, a key material in perovskite solar cells, for measuring carrier cooling and relaxation on femto- and picosecond time scales. Through comparison with transient absorption, we show the links between carrier dynamics and experimental observables of generated harmonics. By highlighting and understanding the interplay of these dynamics, we demonstrate transient optical control over the emission of solid-state high-harmonic generation in MAPbBr3.

Decoherence and Revival in Attosecond Charge Migration Driven by Non-adiabatic Dynamics

Attosecond charge migration is a periodic evolution of the charge density at specific sites of a molecule on a time scale defined by the energy intervals between the electronic states involved. Here, we report the observation of charge migration in neutral silane (SiH₄) in 690 as, its decoherence within 15 fs, and its revival after 40-50 fs, using X-ray attosecond transient absorption spectroscopy. We observe the migration of charge as pairs of quantum beats with a characteristic spectral phase in the transient spectrum, in agreement with theory. The decay and revival of the degree of electronic coherence is found to be a result of both adiabatic and non-adiabatic dynamics in the populated Rydberg and valence states. The experimental results are supported by fully quantum-mechanical ab-initio calculations that include both electronic and nuclear dynamics, which additionally support the experimental evidence that conical intersections can mediate the transfer of electronic coherence from an initial superposition state to another one involving a different lower-lying state.

Single and sequential double ionization of NO radical in intense laser fields

We examine the dependences of the single and double ionization probabilities of NO radical on the angle between the NO axis and the laser polarization direction in an intense laser field (790 nm, 100 fs, 1–10 × 1014 W/cm2) and show that the double ionization is enhanced when the NO axis is parallel to the laser polarization direction. We reveal that the angular dependence of the sequential double ionization probability is determined by the shape of the 5σ orbital of NO+ from which the second photoelectron is emitted in the ionization from NO+ to NO2+. We also reveal that the fast oscillation in the probability of the tunnel ionization of NO originating from a coherent superposition of the two spin–orbit components in the electronic ground X2Π state is described well based on the molecular Ammosov-Delone-Krainov (MO-ADK) theory in which the time evolution of the electron density distribution of the 2π orbital is taken into account.

Rotational dynamics and transitions between Λ-type doubling of NO induced by an intense two-color laser field

We numerically investigate the rotational dynamics of NO in the electronic ground X²Π state induced by an intense two-color laser field (10 TW/cm²) as a function of pulse duration (0.3-25 ps). In the short pulse duration of less than 12 ps, rotational Raman excitation is effectively induced and results in molecular orientation. On the contrary, when the pulse duration is longer than 15 ps, the rotational excitation is suppressed. In addition to the rotational excitation, we find that transitions between Λ-type doubling are induced. Significantly, the maximum coherent wave packet between Λ-type doubling in J = 0.5 is generated using the pulse duration of 19.8 ps. The wave packet changes to the eigenstates of Λ = +1 or -1 alternatively, where Λ is the projection of the electronic orbital angular momentum on the N-O axis, which is regarded as the unidirectional rotation of an unpaired 2π electron around the N-O axis in a space-fixed frame as well as in a molecule-fixed frame. The experimental method to observe the alternation of the rotational direction of the electron around the N-O axis is proposed.

Ultraviolet Pump-Probe Photodissociation Spectroscopy of Electron-Rotation Coupling in Diatomics

The electronic angular momentum projected onto the diatomic axis couples with the angular momentum of the nuclei, significantly affecting the rotational motion of the system under electronic excitations by intense lasers. In this letter, we propose a pump-probe photodissociation scheme for an accurate determination of electron-rotation coupling effects induced by the strong fields. As a showcase we study the CH⁺ molecule excited by a short intense ultraviolet pump pulse to the A¹Π state, which triggers coupled rovibrational dynamics. The dynamics is observed by measuring the kinetic energy release and angular resolved photofragmentation upon photodissociation induced by the time-delayed probe pulse populating the C¹Σ⁺ state. Simulations of the rovibrational dynamics unravel clear fingerprints of the electron-rotation coupling effects that can be observed experimentally. The proposed pump-probe scheme opens new possibilities for the study of ultrafast dynamics following valence electronic transitions with current laser technology, and possible applications are also discussed.

Coupled nuclear and electron dynamics in the vicinity of a conical intersection

Ultrafast optical techniques allow us to study ultrafast molecular dynamics involving both nuclear and electronic motion. To support interpretation, theoretical approaches are needed that can describe both the nuclear and electron dynamics. Hence, we revisit and expand our ansatz for the coupled description of the nuclear and electron dynamics in molecular systems (NEMol). In this purely quantum mechanical ansatz, the quantum-dynamical description of the nuclear motion is combined with the calculation of the electron dynamics in the eigenfunction basis. The NEMol ansatz is applied to simulate the coupled dynamics of the molecule NO₂ in the vicinity of a conical intersection (CoIn) with a special focus on the coherent electron dynamics induced by the non-adiabatic coupling. Furthermore, we aim to control the dynamics of the system when passing the CoIn. The control scheme relies on the carrier envelope phase of a few-cycle IR pulse. The laser pulse influences both the movement of the nuclei and the electrons during the population transfer through the CoIn.

Multi-wave mixing in the high harmonic regime: monitoring electronic dynamics

It has been demonstrated that electronic coherences across many eV can be detected in pump-probe experiments involving high harmonic sources. An additional degree of control over the phase matching can be employed by investigating a more general class of multi-wave mixing. Non-collinear multi-wave mixing of high harmonics with energy (q₁ω₁ + q₂ω₂) can be selectively detected along the direction of (q₁k₁ + q₂k₂). Simulations based on a recently developed semi-perturbative approach show that only the specific harmonic signals with q₁ω₁ close to the energy difference between ground state and excited states are observable when the two input pulses are well separated in time. The coherent dynamics between different states can be selectively tracked by detecting the time-delay dependent signals with different q₁k₁, which can overcome the potential spectral congestion in real experiments. Additionally, such non-collinear geometry can be used to separate the dephasing induced decay and collision induced recovery behaviors of pump-probe high harmonic signal typically observed in the time-resolved high harmonic pump-probe signals.

Detecting electronic coherences by time-domain high-harmonic spectroscopy

Ultrafast spectroscopy is capable of monitoring electronic and vibrational states. For electronic states a few eV apart, an X-ray laser source is required. We propose an alternative method based on the time-domain high-order harmonic spectroscopy where a coherent superposition of the electronic states is first prepared by the strong optical laser pulse. The coherent dynamics can then be probed by the higher-order harmonics generated by the delayed probe pulse. The high nonlinearity typically modeled by the three-step mechanism introduced by Lewenstein and Corkum can serve as a recipe for generation of the coherent excitation with broad bandwidth. The main advantage of the method is that only optical (non-X-ray) lasers are needed. A semiperturbative model based on the Liouville space superoperator approach is developed for the bookkeeping of the different orders of the nonlinear response for the high-order harmonic generation using multiple pulses. Coherence between bound electronic states is monitored in the harmonic spectra from both first- and second-order responses.

Quantum interference and collisional dynamics in excited bounds states revealed by time-resolved pump-high-harmonic-generation-probe spectroscopy

Ultrafast pump-high-harmonic-generation-probe spectroscopy aims to provide a unique observation window into electronic dynamics while using the infrared or visible light sources. While it is widely accepted that the role of excited bound states in high-harmonic generation is negligible, its dynamics play a significant role in time-resolved pump-probe measurements. Here we show that the time-resolved pump-high-harmonic-generation-probe measurement may reveal a significant (up to 20%) contribution of the quantum interference in electron ionization and recombination with atomic system, with the initial or the final state being an excited bound state. Interplay of two dephasing mechanisms of electron-ion and electron-atom collisions yields decay and recovery of the time-resolved signal, respectively, signifying the role of the quantum interference involving excited bound states in recovery mode. Our theory, based on the density matrix Liouville space formalism, is supported by experimental measurements in argon gas.

Signatures of Electronic Structure in Bicircular High-Harmonic Spectroscopy

High-harmonic spectroscopy driven by circularly polarized laser pulses and their counterrotating second harmonic is a new branch of attosecond science which currently lacks quantitative interpretations. We extend this technique to the midinfrared regime and record detailed high-harmonic spectra of several rare-gas atoms. These results are compared with the solution of the Schrödinger equation in three dimensions and calculations based on the strong-field approximation that incorporate accurate scattering-wave recombination matrix elements. A quantum-orbit analysis of these results provides a transparent interpretation of the measured intensity ratios of symmetry-allowed neighboring harmonics in terms of (i) a set of propensity rules related to the angular momentum of the atomic orbitals, (ii) atom-specific matrix elements related to their electronic structure, and (iii) the interference of the emissions associated with electrons in orbitals corotating or counterrotating with the laser fields. These results provide the foundation for a quantitative understanding of bicircular high-harmonic spectroscopy.

Charge migration and charge transfer in molecular systems

The transfer of charge at the molecular level plays a fundamental role in many areas of chemistry, physics, biology and materials science. Today, more than 60 years after the seminal work of R. A. Marcus, charge transfer is still a very active field of research. An important recent impetus comes from the ability to resolve ever faster temporal events, down to the attosecond time scale. Such a high temporal resolution now offers the possibility to unravel the most elementary quantum dynamics of both electrons and nuclei that participate in the complex process of charge transfer. This review covers recent research that addresses the following questions. Can we reconstruct the migration of charge across a molecule on the atomic length and electronic time scales? Can we use strong laser fields to control charge migration? Can we temporally resolve and understand intramolecular charge transfer in dissociative ionization of small molecules, in transition-metal complexes and in conjugated polymers? Can we tailor molecular systems towards specific charge-transfer processes? What are the time scales of the elementary steps of charge transfer in liquids and nanoparticles? Important new insights into each of these topics, obtained from state-of-the-art ultrafast spectroscopy and/or theoretical methods, are summarized in this review.

Monitoring the electron dynamics of the excited state via higher-order spectral minimum

A pump-probe scheme for monitoring the electron dynamics of the excited state has been investigated by numerically solving the two-state time-dependent Schrödinger equation based on the non-Born-Oppenheimer approximation. By adjusting the delay time between a mid-infrared probe pulse and an ultra violet pump pulse, an obvious minimum can be seen in the higher-order harmonic region. With electron probability density distribution, ionization rate and classical simulation, the minimum can be ascribed to the electron localization around one nucleus at larger delay time and represents the electron dynamics of the excited state at the time of ionization. Moreover, the position of the minimum is much more sensitive to the nuclear motion.

Dynamics of valence-shell electrons and nuclei probed by strong-field holography and rescattering

Strong-field photoelectron holography and laser-induced electron diffraction (LIED) are two powerful emerging methods for probing the ultrafast dynamics of molecules. However, both of them have remained restricted to static systems and to nuclear dynamics induced by strong-field ionization. Here we extend these promising methods to image purely electronic valence-shell dynamics in molecules using photoelectron holography. In the same experiment, we use LIED and photoelectron holography simultaneously, to observe coupled electronic-rotational dynamics taking place on similar timescales. These results offer perspectives for imaging ultrafast dynamics of molecules on femtosecond to attosecond timescales.

Capturing ultrafast molecular dynamics is difficult as the process involves coupled and very fast motions of electrons and nuclei. Here the authors study non-adiabatic dynamics in the NO molecule using strong-field photoelectron holography to shed light on the valence-shell electron dynamics.

Strong-field-induced wave packet dynamics in carbon dioxide molecule

Temporal evolution of electronic and nuclear wave packets created in strong-field excitation of the carbon dioxide molecule is studied employing momentum-resolved ion spectroscopy and channel-selective Fourier analysis. Combining the data obtained with two different pump-probe set-ups, we observed signatures of vibrational dynamics in both, ionic and neutral states of the molecule. We consider far-off-resonance two-photon Raman scattering to be the most likely mechanism of vibrational excitation in the electronic ground state of the neutral CO₂. Using the measured phase relation between the time-dependent yields of different fragmentation channels, which is consistent with the proposed mechanism, we suggest an intuitive picture of the underlying vibrational dynamics. For ionic states, we found signatures of both, electronic and vibrational excitations, which involve the ground and the first excited electronic states, depending on the particular final state of the fragmentation. While our results for ionic states are consistent with the recent observations by Erattupuzha et al. [J. Chem. Phys.144, 024306 (2016)], the neutral state contribution was not observed there, which we attribute to a larger bandwidth of the 8 fs pulses we used for this experiment. In a complementary measurement employing longer, 35 fs pulses in a 30 ps delay range, we study the influence of rotational excitation on our observables, and demonstrate how the coherent electronic wave packet created in the ground electronic state of the ion completely decays within 10 ps due to the coupling to rotational motion.

Direct observation of an attosecond electron wave packet in a nitrogen molecule

Capturing electron motion in a molecule is the basis of understanding or steering chemical reactions. Nonlinear Fourier transform spectroscopy using an attosecond-pump/attosecond-probe technique is used to observe an attosecond electron wave packet in a nitrogen molecule in real time. The 500-as electronic motion between two bound electronic states in a nitrogen molecule is captured by measuring the fragment ions with the same kinetic energy generated in sequential two-photon dissociative ionization processes. The temporal evolution of electronic coherence originating from various electronic states is visualized via the fragment ions appearing after irradiation of the probe pulse. This observation of an attosecond molecular electron wave packet is a critical step in understanding coupled nuclear and electron motion in polyatomic and biological molecules to explore attochemistry.

The sensitivities of high-harmonic generation and strong-field ionization to coupled electronic and nuclear dynamics

The sensitivities of high-harmonic generation (HHG) and strong-field ionization (SFI) to coupled electronic and nuclear dynamics are studied, using the nitric oxide (NO) molecule as an example. A coherent superposition of electronic and rotational states of NO is prepared by impulsive stimulated Raman scattering and probed by simultaneous detection of HHG and SFI yields. We observe a fourfold higher sensitivity of high-harmonic generation to electronic dynamics and attribute it to the presence of inelastic quantum paths connecting coherently related electronic states [Kraus et al., Phys. Rev. Lett.111, 243005 (2013)]. Whereas different harmonic orders display very different sensitivities to rotational or electronic dynamics, strong-field ionization is found to be most sensitive to electronic motion. We introduce a general theoretical formalism for high-harmonic generation from coupled nuclear-electronic wave packets. We show that the unequal sensitivities of different harmonic orders to electronic or rotational dynamics result from the angle dependence of the photorecombination matrix elements which encode several autoionizing and shape resonances in the photoionization continuum of NO. We further study the dependence of rotational and electronic coherences on the intensity of the excitation pulse and support the observations with calculations.