Two-pulse field-free orientation reveals anisotropy of molecular shape resonance

Odd-even harmonic emission from oriented NO molecule with nodal planes

We investigate odd-even high-harmonic generation (HHG) of oriented asymmetric molecule NO. We focus on the effect of the structure of the molecule with nodal planes on the generation mechanism of odd-even harmonics parallel and perpendicular to the laser polarization. Our numerical simulations show that the relative yields of parallel and perpendicular odd-even harmonics are sensitive to the orientation of the molecule. Our analyses reveal that the nodal plane of the molecule plays an important role in the emission mechanism of odd-even harmonics, remarkably changing the main emission channels of odd-even HHG. This role can be well understood through a simple odd-even HHG model that considers the symmetry of the laser-driven asymmetric system. Cases for different degrees of orientation and for asymmetric molecules with other symmetry such as CO are also addressed.

Quantum Electrodynamics in High-Harmonic Generation: Multitrajectory Ehrenfest and Exact Quantum Analysis

High-harmonic generation (HHG) is a nonlinear process in which a material sample is irradiated by intense laser pulses, causing the emission of high harmonics of incident light. HHG has historically been explained by theories employing a classical electromagnetic field, successfully capturing its spectral and temporal characteristics. However, recent research indicates that quantum-optical effects naturally exist or can be artificially induced in HHG, such as entanglement between emitted harmonics. Even though the fundamental equations of motion for quantum electrodynamics (QED) are well-known, a unifying framework for solving them to explore HHG is missing. So far, numerical solutions have employed a wide range of basis-sets, methods, and untested approximations. Based on methods originally developed for cavity polaritonics, here we formulate a numerically accurate QED model consisting of a single active electron and a single quantized photon mode. Our framework can, in principle, be extended to higher electronic dimensions and multiple photon modes to be employed in ab initio codes for realistic physical systems. We employ it as a model of an atom interacting with a photon mode and predict a characteristic minimum structure in the HHG yield vs phase-squeezing. We find that this phenomenon, which can be used for novel ultrafast quantum spectroscopies, is partially captured by a multitrajectory Ehrenfest dynamics approach, with the exact minima position sensitive to the level of theory. On the one hand, this motivates using multitrajectory approaches as an alternative for costly exact calculations. On the other hand, it suggests an inherent limitation of the multitrajectory formalism, indicating the presence of entanglement and true quantum effects (especially prominent for atomic and molecular resonances). Our work creates a roadmap for a universal formalism of QED-HHG that can be employed for benchmarking approximate theories, predicting novel phenomena for advancing quantum applications, and for the measurements of entanglement and entropy.

Electronic Coherences Excited by an Ultra Short Pulse Are Robust with Respect to Averaging over Randomly Oriented Molecules as Shown by Singular Value Decomposition

We report a methodology for averaging quantum photoexcitation vibronic dynamics over the initial orientations of the molecules with respect to an ultrashort light pulse. We use singular value decomposition of the ensemble density matrix of the excited molecules, which allows the identification of the few dominant principal molecular orientations with respect to the polarization direction of the electric field. The principal orientations provide insights into the specific stereodynamics of the corresponding principal molecular vibronic states. The massive compaction of the vibronic density matrix of the ensemble of randomly oriented pumped molecules enables a most efficient fully quantum mechanical time propagation scheme. Two examples are discussed for the quantum dynamics of the LiH molecule in the manifolds of its electronically excited Σ and Π states. Our results show that electronic and vibrational coherences between excited states of the same symmetry are resilient to averaging over an ensemble of molecular orientations and can be selectively excited at the ensemble level by tuning the pulse parameters.

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.

Quantum control of field-free molecular orientation

Generating field-free (non-stationary) orientation of molecules in space has been a longstanding goal in the field of quantum control of molecular rotation, which has significant applications in physical chemistry, chemical physics, strong-field physics, and quantum information science. In this Perspective, we review and examine several representative control schemes developed in recent years and implemented in theoretical and experimental areas for generating field-free orientation of molecules. By conducting numerical simulations of different control schemes on the same molecular system, we demonstrate that quantum coherent control, specifically targeting a limited number of the lowest-lying rotational levels to achieve an optimal superposition, can result in a high degree of orientation. To this end, we provide an overview of our latest developed analytical method, which enables the precise design of terahertz field parameters through resonant excitation. This design approach facilitates the attainment of desired field-free orientations by optimizing the amplitudes and phases of rotational wave functions for the selected rotational levels. Finally, we outlook the significance of such progress in multiple frontier research fields, highlighting its potential applications in ultracold physics, quantum computation, quantum simulation, and quantum metrology.

Effects of Autoionizing Resonances on Wave-Packet Dynamics Studied by Time-Resolved Photoelectron Spectroscopy

We report a combined experimental and theoretical study on the effect of autoionizing resonances in time-resolved photoelectron spectroscopy. The coherent excitation of N_{2} by ∼14.15  eV extreme-ultraviolet photons prepares a superposition of three dominant adjacent vibrational levels (v^{'}=14-16) in the valence b^{'} ^{1}Σ_{u}^{+} state, which are probed by the absorption of two or three near-infrared photons (800 nm). The superposition manifests itself as coherent oscillations in the measured photoelectron spectra. A quantum-mechanical simulation confirms that two autoionizing Rydberg states converging to the excited A ^{2}Π_{u} and B ^{2}Σ_{u}^{+} N_{2}^{+} cores are accessed by the resonant absorption of near-infrared photons. We show that these resonances apply different filters to the observation of the vibrational wave packet, which results in different phases and amplitudes of the oscillating photoelectron signal depending on the nature of the autoionizing resonance. This work clarifies the importance of resonances in time-resolved photoelectron spectroscopy and particularly reveals the phase of vibrational quantum beats as a powerful observable for characterizing the properties of such resonances.

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.

Field-free molecular orientation by delay- and polarization-optimized two fs pulses

Unless the molecular axis is fixed in the laboratory frame, intrinsic structural information of molecules can be averaged out over the various rotational states. The macroscopic directional properties of polar molecules have been controlled by two fs pulses with an optimized delay. In the method, the first one-color laser pulse provokes molecular alignment. Subsequently, the molecular sample is irradiated with the second two-color laser pulse, when the initial even-J states are aligned, and the odd-J states are anti-aligned in the thermal ensemble. The second pulse selectively orients only the aligned even-J states in the same direction, which results in significant enhancement of the net degree of orientation. This paper reports the results of simulations showing that the two-pulse technique can be even more powerful when the second pulse is cross-polarized. This study shows that the alignment and orientation can be very well synchronized temporally because the crossed field does not disturb the preformed alignment modulation significantly, suggesting that the molecules are very well confined in the laboratory frame. This cross-polarization method will serve as a promising technique for studying ultrafast molecular spectroscopy in a molecule-fixed frame.

Steering the outcome of a photochemical reaction-An in silico experiment on the H2CSO sulfine using few-femtosecond dump pulses

We propose a pump-dump control scheme using sub-10 fs pulses to enhance the photochemical formation of the three-membered C-S-O ring oxathiirane from the parent H₂CSO sulfine molecule. The ultrashort nature of the pulses is essential to promptly alter the photoinduced dynamics, e.g., while a bond is elongating, which is key to selectively form the oxathiirane by radiative dumping. We carried out an in silico pump-dump experiment with excited-state dynamics simulations that include the interaction with electric field of the pump and dump pulses. By applying the dump pulse when the CS bond is elongating, the population transferred to the ground state will form the oxathiirane with a branching ratio of 4, much higher than the one solely due to nonradiative relaxation (0.66). The overall oxathiirane yield can be increased by up to 17% when the 6 fs IR dump pulse is applied at a delay time of 47 fs.

Sub-Femtosecond Stark Control of Molecular Photoexcitation with Near Single-Cycle Pulses

Electric fields can tailor molecular potential energy surfaces by interaction with the electronic state-dependent molecular dipole moment. Recent developments in optics have enabled the creation of ultrashort few-cycle optical pulses with precise control of the carrier envelope phase (CEP) that determines the offset of the maxima in the field and the pulse envelope. This opens news ways of controlling ultrafast molecular dynamics by exploiting the CEP. In this work, we show that the photoabsorption efficiency of oriented H₂CSO (sulfine) can be controlled by tuning the CEP. We further show that this control emanates from a resonance condition related to Stark shifting of the electronic energy levels.

Carrier-envelope phase-dependent molecular high-order harmonic generation from H2+ in a multi-cycle regime

Carrier-envelope phase (CEP) dependence of high-order harmonic generation (HHG) from H2+ in a multi-cycle laser pulse is investigated by solving the non-Born-Oppenheimer time-dependent Schrödinger equation (TDSE). It is found that high harmonics in the plateau exhibit counterintuitive frequency modulation (FM) as the CEP of the multi-cycle laser varies. Based on the classical electron trajectories and time-frequency analysis, this multi-cycle CEP-dependent FM is demonstrated to result from the interference of half-cycle HHG radiations, which is modulated by laser-driven nuclear motion. The mechanism of the CEP-dependent FM is further confirmed by simulations based on a simple algorithm in the time domain, which satisfactorily reproduces the TDSE results. The CEP-dependent FM encodes rich information on the correlated electron and nuclear dynamics, which paves the way for probing nuclear motion with attosecond resolution.

Routes of odd-even harmonic emission from oriented polar molecules

We study odd-even high-harmonic generation (HHG) from oriented asymmetric molecules with different symmetries in strong laser fields. A model based on strong-field approximations is used which allows us to resolve the contributions of different emission routes to odd-even HHG. The comparison between the HHG yields of all routes versus one certain route demonstrates that the routes in which the electron ionizes from the gerade component of the asymmetric orbital contribute mainly to odd-even HHG. We show that the potential mechanism is associated with effects of intramolecular interference in tunneling ionization as the bound electron passes through the barrier formed by the laser field and the asymmetric Coulomb potential. The influences of different emission routes on asymmetric orbital imagining with odd-even HHG are also addressed.

Time-dependent analysis of the mixed-field orientation of molecules without rotational symmetry

We present a theoretical study of the mixed-field orientation of molecules without rotational symmetry. The time-dependent one-dimensional and three-dimensional orientation of a thermal ensemble of 6-chloropyridazine-3-carbonitrile molecules in combined linearly or elliptically polarized laser fields and tilted dc electric fields is computed. The results are in good agreement with recent experimental results of one-dimensional orientation for weak dc electric fields [J. L. Hansen, J. Chem. Phys. 139, 234313 (2013)]. Moreover, they predict that using elliptically polarized laser fields or strong dc fields, three-dimensional orientation is obtained. The field-dressed dynamics of excited rotational states is characterized by highly non-adiabatic effects. We analyze the sources of these non-adiabatic effects and investigate their impact on the mixed-field orientation for different field configurations in mixed-field-orientation experiments.

Strong field transient manipulation of electronic states and bands

In the present review, laser fields are so strong that they become part of the electronic potential, and sometimes even dominate the Coulomb contribution. This manipulation of atomic potentials and of the associated states and bands finds fascinating applications in gases and solids, both in the bulk and at the surface. We present some recent spectacular examples obtained within the NCCR MUST in Switzerland.

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.

Pure Even Harmonic Generation from Oriented CO in Linearly Polarized Laser Fields

The first high harmonic spectrum containing only the odd orders was observed in experiments 30 years ago. However, a spectrum containing pure even harmonics has never been observed. We investigate the generation of pure even harmonics from oriented CO molecules in linearly polarized laser fields employing the time-dependent density-functional theory. We find that the even harmonics, with no odd orders, are generated with the polarization perpendicular to the laser polarization when the molecular axis of CO is perpendicular to the laser polarization. The generation of pure even harmonics reveals a type of dipole acceleration originating from the permanent dipole moment. This phenomenon exists in all systems with permanent dipole moments, including bulk crystal and polyatomic molecules.

Attosecond Probing of Nuclear Dynamics with Trajectory-Resolved High-Harmonic Spectroscopy

We report attosecond-scale probing of the laser-induced dynamics in molecules. We apply the method of high-harmonic spectroscopy, where laser-driven recolliding electrons on various trajectories record the motion of their parent ion. Based on the transient phase-matching mechanism of high-order harmonic generation, short and long trajectories contributing to the same harmonic order are distinguishable in both the spatial and frequency domains, giving rise to a one-to-one map between time and photon energy for each trajectory. The short and long trajectories in H_{2} and D_{2} are used simultaneously to retrieve the nuclear dynamics on the attosecond and ångström scale. Compared to using only short trajectories, this extends the temporal range of the measurement to one optical cycle. The experiment is also applied to methane and ammonia molecules.

Bicircular High-Harmonic Spectroscopy Reveals Dynamical Symmetries of Atoms and Molecules

We introduce bicircular high-harmonic spectroscopy as a new method to probe dynamical symmetries of atoms and molecules and their evolution in time. Our approach is based on combining a circularly polarized femtosecond fundamental field of frequency ω with its counterrotating second harmonic 2ω. We demonstrate the ability of bicircular high-harmonic spectroscopy to characterize the orbital angular momentum symmetry of atomic orbitals. We further show that breaking the threefold rotational symmetry of the generating medium-at the level of either the ensemble or that of a single molecule-results in the emission of the otherwise parity-forbidden frequencies 3qω  (q∈N), which provide a background-free probe of dynamical molecular symmetries.

Nonadiabatic Electron Dynamics in Orthogonal Two-Color Laser Fields with Comparable Intensities

We theoretically investigate the nonadiabatic subcycle electron dynamics in orthogonally polarized two-color laser fields with comparable intensities. The photoelectron dynamics is simulated by exact solution to the 3D time-dependent Schrödinger equation, and also by two other semiclassical methods, i.e., the quantum trajectory Monte Carlo simulation and the Coulomb-corrected strong field approximation. Through these methods, we identify the underlying mechanisms of the subcycle electron dynamics and find that both the nonadiabatic effects and the Coulomb potential play very important roles. The contribution of the nonadiabatic effects manifest in two aspects, i.e., the nonadiabatic ionization rate and the nonzero initial velocities at the tunneling exit. The Coulomb potential has a different impact on the electrons' trajectories for different relative phases between the two pulses.

Observation of laser-induced electronic structure in oriented polyatomic molecules

All attosecond time-resolved measurements have so far relied on the use of intense near-infrared laser pulses. In particular, attosecond streaking, laser-induced electron diffraction and high-harmonic generation all make use of non-perturbative light-matter interactions. Remarkably, the effect of the strong laser field on the studied sample has often been neglected in previous studies. Here we use high-harmonic spectroscopy to measure laser-induced modifications of the electronic structure of molecules. We study high-harmonic spectra of spatially oriented CH3F and CH3Br as generic examples of polar polyatomic molecules. We accurately measure intensity ratios of even and odd-harmonic orders, and of the emission from aligned and unaligned molecules. We show that these robust observables reveal a substantial modification of the molecular electronic structure by the external laser field. Our insights offer new challenges and opportunities for a range of emerging strong-field attosecond spectroscopies.

Controlling attosecond angular streaking with second harmonic radiation

High harmonic generation, which produces a coherent burst of radiation every half cycle of the driving field, has been combined with ultrafast wavefront rotation to create a series of spatially separated attosecond pulses, called the attosecond lighthouse. By adding a coherent second harmonic beam with polarization parallel to the fundamental, we decrease the generating frequency from twice per optical cycle to once. The increased temporal separation increases the pulse contrast. By scanning the carrier envelope phase, we see that the signal is 2π periodic.

Two-state wave packet for strong field-free molecular orientation

We demonstrate strong laser-field-free orientation of absolute-ground-state carbonyl sulfide molecules. The molecules are oriented by the combination of a 485-ps-long nonresonant laser pulse and a weak static electric field. The edges of the laser pulse create a coherent superposition of two rotational states resulting in revivals of strong transient molecular orientation after the laser pulse. The experimentally attained degree of orientation ⟨cosθ⟩≈0.6 corresponds to the theoretical maximum for mixing of the two states. Switching off the dc field would provide the same orientation completely field free.

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.