Gas-phase electron diffraction techniques have served as prominent methods for probing the structures of molecules. However, these methods may not be effective in distinguishing structures between molecular isomers due to their limited sensitivity to nonadjacent bond structures and electronic configurations. Laser-induced electron diffraction (LIED) offers a compelling alternative as the yield of the self-imaging electron highly depends on the shape of valence orbitals, thereby creating distinct diffraction patterns for isomers. Here, we present theoretical and experimental evidence demonstrating the capability of LIED to distinguish between n-butane and isobutane. The underlying principle is elucidated through modeling the multiorbital tunnel ionization of the molecules and the subsequent rescattering of the ionized electron with the molecule. Our findings highlight LIED as a powerful technique for identifying molecular isomers and shed light on its potential for simultaneously probing the nuclear and electronic structure of a molecule. Although gas-phase electron diffraction has served as a prominent method for probing molecular structure, it may not be effective in distinguishing structures between molecular isomers. Here, the authors report on laser-induced electron diffraction (LIED) as an alternative approach, showing that it can distinguish between n-butane and isobutane unambiguously due to its sensitivity to both molecular geometry and electronic structure, highlighting its capabilities as a background-free probe for nuclear and electron dynamics in molecules.

Generating ever-shorter and brighter light pulses is a central goal of ultrafast science, enabling coherent control and observation of electron dynamics on their natural timescale. State-of-the-art isolated attosecond pulse generation currently achieves pulse durations of 40-50 attoseconds. Here we demonstrate isolated attosecond light pulses with durations of 18 attoseconds, via high-order harmonic generation driven by a post-compressed industrial-grade Yb laser system. The high-harmonic spectrum spans photon energies from 50 to 320 eV, covering the carbon K-edge, with a calibrated photon flux exceeding 1012 photons per second. Pulse durations were characterized by angle-resolved photoelectron streaking in helium and optimized using a series of filters with different thicknesses to compensate the attochirp. We further developed a robust, fast-converging pulse-retrieval algorithm capable of reconstructing broadband isolated attosecond pulses and double pulses. These results establish Yb-laser-driven high-order harmonic generation as a powerful platform for bright isolated attosecond sources and next-generation ultrafast spectroscopy.

The carrier-envelope offset phase (CEP) of a few-cycle optical pulse is commonly used to control electron dynamics on the attosecond timescale, whereas lasing spectra from transitions between rotational states are generally emitted over much longer durations, typically nanoseconds. Here, we demonstrate CEP control of the rotational lasing spectra corresponding to the transition from B 2 Σ u + ( 0 ) to X 2 Σ g + ( 1 ) in N 2 + cations, transforming its lineshape from a symmetric Lorentzian profile to an asymmetric Fano type-and vice versa. This lineshape modulation arises from the interference between the B-X coherence initiated by the main pulse and the supercontinuum (self seed) by self-phase modulation, resembling an "f-to-3f" interferometry. Additionally, for lasing lines with lower rotational quantum numbers, we observe a stronger coupling between adjacent lasing peaks, which originates from the amplification of both even- and odd-order rotational coherent emission lines. Our study presents a general framework for controlling lasing lineshapes and provides new insights into sub-optical-cycle dynamics in air lasing.

The concept of using photoelectron interferometry in short laser fields to probe electron dynamics and target structures was introduced more than two decades ago. However, the quality of experimental data has remained insufficient for quantitative analysis, largely due to the instability of few-cycle Ti:sapphire laser pulses-the current workhorse of short pulses. Here, we report the first systematic strong-field ionization experiments performed with industrial-grade, carrier-envelope-phase stabilized, near-single-cycle Yb lasers. By measuring photoelectron momentum distributions in the direct-ionization regime, we show that single-cycle cosine-shaped pulses can separate and enhance both spider-leg and fishbone holographic structures. The spider-leg structure enables extraction of the electron scattering phase from the Ar atomic potential-information typically accessible through attosecond metrology-while the fishbone structure reveals the orbital-parity contrast between Ar atoms and nitrogen molecules. Our measurements are quantitatively reproduced by both semiclassical Herman-Kluk-propagator and ab initio simulations, paving the way for precision studies of electron-molecule scattering with widely accessible industrial-grade lasers.

The spatiotemporal properties of a multicolor laser waveform during its propagation in a gas medium are of great interest, but they cannot be obtained using traditional characterization methods for ultrashort laser pulses. In this work, we demonstrate that high-order harmonic generation (HHG) spectroscopy provides an opportunity to obtain this information. To this end, we first show that the experimentally measured HHG spectra of Ne atoms, generated using a long-duration three-color synthesizer in a long gas cell, can be reproduced by our simulation, and continuum harmonics appear in both experiment and simulation. By synthesizing an isolated attosecond pulse from the continuum harmonics, the spatiotemporal reshaping of the driving laser waveform can be explored. Next, by varying the time delay between two of the three colors, we extract the slope of the high-energy photons. In theory, our results demonstrate that the spatiotemporal reshaping of the three-color laser waveform can be identified through the relationship between the slope and the cutoff energy, with the single-atom response serving as a reference. This approach is anticipated to significantly expand the applications of multicolor lasers across diverse research fields.

We investigate strong-field-induced electronic coherences in argon and molecular nitrogen ions created by high-intensity, few-cycle infrared laser pulses. This is a step toward the long-sought goal of strong-field coherent control in molecular chemistry. We employ high-intensity, few-cycle infrared laser pulses in a pump-probe setup to investigate a recent prediction that electronic coherences in nitrogen molecules change the ion yields versus pump-probe delay. [Yuen et al., Phys. Rev. A 109, L011101 (2024)]. The predicted coherence signals in molecular nitrogen could not be resolved above the optical interference of the pump and probe pulses; a simultaneous measurement clearly resolved the induced cation fine-structure coherence in strong-field-ionized argon. The results of our comparison with simulations suggest that optical interference effects manifest differently in each ionic species and must be carefully accounted for when interpreting experimental data. We find that nonsequential double ionization in the low-intensity region of the focal volume can reduce the visibility of coherence generated by two-pulse sequential ionization, and we quantify the importance of pulse shape and spectral characteristics for isolating the desired coherence signals.

Generating ever-shorter and brighter light pulses has long been a central pursuit in ultrafast science, as it benchmarks our ability to create and manipulate the coherence on the intrinsic timescale of sub-atomic electron motion. The current state-of-the-art in attosecond pulse generation reaches durations of 40-50 attoseconds (1 as = 10^-18 seconds), produced via high-order harmonic generation (HHG) driven by secondary mid-infrared light sources. However, these sources often suffer from low stability and poor HHG conversion efficiency. In this work, we demonstrate the generation of 25±2 attosecond light pulses, a new world record for the shortest light pulse, driven by a post-compressed, industrial-grade Yb-based laser system. The resulting high-harmonic spectrum spans photon energies from 50 eV to 320 eV, covering the carbon K-edge, with a calibrated photon flux exceeding 10^12 photons per second, approximately three orders of magnitude higher than previous studies. The pulse duration was characterized using an angle-resolved photoelectron streaking camera on helium atoms and systematically optimized through the use of dielectric filters of varying thicknesses to compensate the attochirp. Our study reaches the threshold of one atomic unit of time (24.2 attoseconds), the boundary between atomic and ionic physics, opening the door to resolving exciting ionic quantum dynamics with tabletop lasers.

Excitation or ionization of a molecule by ultrafast laser pulses can create a superposition of electronic states, whose dynamics is influenced by the interplay of electronic coherence and nuclear motion, resulting in charge migration and possibly charge transfer. Probing the vibronic coherence is therefore vital to monitoring electronic dynamics and controlling chemical reactivity, as recently demonstrated in molecules via attosecond transient absorption spectroscopy (ATAS). However, theories supporting the interpretation of ATAS experiments neglect the effects of molecular rotation, often leading to inaccurate interpretation of experimental data. Here, we develop a comprehensive theory for ATAS of molecules encompassing the entire pump-probe process. Applying the theory to N2, we demonstrate that the emergence of coherent signals critically depends on the consideration of molecular rotation. This work contributes to close the gap between theory and ATAS experiments, paving the way for monitoring electronic motion and controlling chemical reactivity in diverse molecular systems. Attosecond transient absorption spectroscopy (ATAS) is a powerful scheme for monitoring the vibronic coherences that enables real-time observation of electronic motion, but the role of molecular rotation is usually neglected. The authors propose a theory fully accounting for molecular rotation in ATAS, closing the gap between theory and ATAS experiments.

High-harmonic generation from a gas target exhibits sharp spectral features and rapid phase variation near the Cooper minimum. By applying spectral filtering, shaped isolated attosecond pulses can be generated where the pulse is split into two in the time domain. Using such shaped extreme-ultraviolet (XUV) pulses, we theoretically study attosecond transient absorption (ATA) spectra of helium 2s2p autoionizing state which is resonantly coupled to the 2s2 dark state by a time-delayed infrared laser. Our simulations show that the asymmetric 2s2p Fano line shape can be readily tuned into symmetric Lorentzian within the time delay of a few tens of attoseconds. Such efficient control is due to the destructive interference in the generation of the 2s2p state when it is excited by a strongly shaped XUV pulse. This is to be compared to prior experiments where tuning the line shape of a Fano resonance would take tens of femtoseconds. We also show that the predicted ATA spectral line shape can be observed experimentally after propagation in a gas medium. Our results suggest that strongly shaped attosecond XUV pulses offer the opportunity for controlling and probing fine features of narrow resonances on the few-ten attoseconds timescale.

Real-time visualization of molecular transformations is a captivating yet challenging frontier of ultrafast optical science and physical chemistry. While ultrafast x-ray and electron diffraction methods can achieve the needed subangstrom spatial resolution, their temporal resolution is still limited to hundreds of femtoseconds, much longer than the few femtoseconds required to probe real-time molecular dynamics. Here, we show that high-order harmonics generated by intense femtosecond lasers can be used to image molecules with few-ten-attosecond temporal resolution and few-picometer spatial resolution. This is achieved by exploiting the sensitive dependence of molecular recombination dipole moment to the geometry of the molecule at the time of harmonic emission. In a proof-of-principle experiment, we have applied this high-harmonic structure imaging (HHSI) method to monitor the structural rearrangement in NH_{3}, ND_{3}, and N_{2} from one to a few femtoseconds after the molecule is ionized by an intense laser. Our findings establish HHSI as an effective approach to resolve molecular dynamics with unprecedented spatiotemporal resolution, which can be extended to trace photochemical reactions in the future.

An all-optical method for directly reconstructing the spectral phase of an isolated attosecond pulse (IAP) has been proposed recently [New J. Phys. 25, 083003 (2023)]. This method is based on high-harmonic-generation (HHG) streaking spectra generated by an IAP and a time-delayed intense infrared (IR) laser, which can be accurately simulated by an extended quantitative rescattering model. Here, we extend the retrieval algorithm in this method to successfully retrieve the spectral phase of a shaped IAP, which has a spectral minimum, a phase jump about pi, and a "split" temporal profile. We then reconstruct the carrier-envelope phase of the IR laser from HHG streaking spectra. Finally, we discuss retrieval of the phase of high harmonics by the intense IR laser alone using the Fourier transform of HHG streaking spectra.

A density matrix approach was recently developed by Yuen and Lin to study the dissociative sequential double ionization (SDI) of ${\text{N}}_{2}$ molecules induced by an intense few-cycle infrared laser pulse [Phys. Rev. A 106, 023120 (2022)]. Despite the positions and relative ratios of peaks in the simulated kinetic energy release (KER) spectrum agreeing very well with experiments, the experimental KER spectrum is considerably broader than that obtained from the simulation where both laser couplings between ${\text{N}}_{2}{}^{2+}$ states and the nuclear vibration distribution of neutral ${\text{N}}_{2}$ molecules were neglected. Here, we revisit to simulate the experiment by Voss et al. [J. Phys. B: At. Mol. Opt. Phys. 37, 4239 (2004)] and Wu et al. [J. Phys. Chem. A 114, 6751 (2010)] and find that the agreement between the simulated KER spectra and the experiments is improved significantly by considering the laser couplings between ${\text{N}}_{2}{}^{2+}$ states and nuclear vibration distribution of neutral ${\text{N}}_{2}$ molecules. This work provides further insights into the SDI dynamics and the influences of nuclear motion on the SDI of molecules.

Understanding of strong -field sequential double ionization (SDI) of molecules by a highly intense infrared laser pulse could be the key to observing electron motion in molecules in the attosecond to femtosecond timescale. Based on a novel density matrix approach for SDI (DM -SDI), a recent theoretical study [Yuen and Lin, Phys. Rev. A 109, L011101 (2024)] has shown that SDI can be used as a probe to monitor the changes in vibronic coherence in homonuclear diatomic molecules. In this article, we extend the DM -SDI model to general molecules that could possess permanent dipole moments and arbitrary symmetry. We apply the model to SDI of a water molecule and identify the formation pathway of individual dication states. We further deduce that kinetic energy release spectra from two- and three -body fragments could carry the signature of vibronic coherence between the lowest two states of the water cation. Our results suggest that observables from the SDI probe can be interpreted intuitively with only the knowledge of electronic structures of populated ionic states, making the SDI probe to be a highly desirable probing scheme for vibronic coherence in generic molecules.

In recent years, significant advancements in high-repetition-rate, high-average-power mid-infrared laser pulses have enabled the generation of tabletop high-flux coherent soft x-ray harmonics for photon-hungry experiments. However, for practical applications, it is crucial to effectively filter out the driving beam from the high harmonics. In this study, we leverage the distinctive properties of a Bessel-Gauss (BG) beam to introduce a novel approach for spatial filtering, specifically targeting soft x-ray harmonics, releasing with a high-photon flux simultaneously. Our simulations reveal that by finely adjusting the focus geometry and gas pressure, the BG beam naturally adopts an annular shape, emitting high harmonics with minimal divergence in the far field. To achieve complete spatial separation of the driving beam and harmonic emissions, we pinpoint the optimal gas pressure and focusing geometry, particularly under overdriven laser intensities, for achieving good phase matching of harmonic emissions from short-trajectory electrons within the gas medium when the exact ionization level is higher than the "critical" value. Additionally, we establish scaling relations for sustaining optimal phase-matching conditions crucial for spatially separating the driving laser and the high-harmonic field, especially as the wavelength of the driving laser increases. Furthermore, our analysis demonstrates a substantial enhancement of harmonic yields by at least one order of magnitude compared to a truncated Gaussian annular beam. We also show that under accessible experimental conditions, soft x-ray photon flux up to 1010 photons/s at 250 eV can be achieved. The utilization of the BG beam opens up a promising pathway for the development of high-flux attosecond soft x-ray light sources, poised to serve a wide range of applications.

We propose a novel scheme for probing vibronic coherence in charge migration in molecules utilizing strong field sequential double ionization. To demonstrate the feasibility of this approach, we perform full simulations of a pump-probe scheme employing few-cycle intense infrared pulses for N$_2$ and O$_2$. We predict that the vibronic coherence between the pumped states will be directly imprinted in experimental observables such as kinetic energy release spectra and branching ratios of the dissociative dications. Our simulations are based on the recently developed DM-SDI model, which is capable of efficiently accounting for molecular orientations and enabling direct comparison with experimental results. Our findings strongly encourage the use of this probing scheme in future charge migration experiments.

High-order harmonics have been widely used as reliable tabletop coherent radiation sources recently, but their applications have often been limited by the available pulse energy. Here, we report that by using an overdriven intense laser in a long waveguide with high-pressure gas, phase matching can be achieved in three distinct “regimes”. In the third regime, favorable phase matching is achieved at near-axis positions to enhance harmonic yields. Our results are supported by a full theoretical analysis, and we demonstrate that coupling of the driving laser with the high-order waveguide modes (instead of the fundamental mode used in most prior experiments) is responsible for achieving phase matching. Furthermore, we establish that this phase matching (and harmonic enhancement) is robust, and a scaling relation is derived for the necessary waveguide and gas parameters, allowing our predictions to be tested immediately in any laboratory today.

Abstract. In quantum mechanics, when an electron is quickly ripped off from a molecule, a superposition of new eigenstates of the cation creates an electron wave packet that governs the charge flow inside, which has been called charge migration (CM). Experimentally, extracting such dynamics at its natural (attosecond) timescale is quite difficult. We report the first such experiment in a linear carbon-chain molecule, butadiyne (C4H2), via high-harmonic spectroscopy (HHS). By employing advanced theoretical and computational tools, we showed that the wave packet and the CM of a single molecule are reconstructed from the harmonic spectra for each fixed-in-space angle of the molecule. For this one-dimensional molecule, we calculate the center of charge   ⟨  x  ⟩    (  t  )   to obtain vcm, to quantify the migration speed and how it depends on the orientation angle. The findings also uncover how the electron dynamics at the first few tens to hundreds of attoseconds depends on molecular structure. The method can be extended to other molecules where the HHS technique can be employed.

We investigate the role of the Porras factor (or laser focusing effect) on the macroscopic high-order harmonic generation (HHG) driven by a focused broadband few-cycle laser beam. By employing a non-adiabatic phase-matching analysis method, we reveal that phase mismatch due to the induced-dipole phase varies with the Porras factor, which is dominant in phase matching at low gas pressure. We also find that in a strongly ionized medium when gas pressure is high, the nonlinear propagation is dominated by a plasma effect such that the focusing effect is mitigated, resulting in similar poor phase matching of HHG regardless of the Porras factor. Our results are expected to assist experimentalists identifying optimal conditions for HHG using ultrashort laser pulses.

We present a simple and general coherence model for multiorbital tunnel ionization of molecules, which we incorporate into our previously developed density matrix approach for sequential double ionization [Yuen and Lin, Phys. Rev. A 106, 023120 (2022)]. The influence of this coherence is investigated through simulations of single ionization and sequential double ionization of N$_2$ and O$_2$ using few-cycle near-infrared laser pulses. In the case of single ionization, our results reveal the crucial role played by this coherence in generating population inversion in N$_2^+$, suggesting a potential mechanism for air lasing. Regarding sequential double ionization, we observe only minor changes in the kinetic energy release spectra when the coherence is included, while noticeable differences in the angle-dependent dication yield for both N$_2$ and O$_2$ are found. Based on these findings, we recommend the inclusion of multiorbital tunnel ionization coherence in models for single ionization of general molecules, while suggesting that it can be safely neglected in the case of sequential double ionization.

High-order harmonics generated by a long intense femtosecond laser are known experimentally to create attosecond pulse trains (APTs). In the time domain, an APT consists of a sequence of sharp attosecond bursts that are equally separated by each half optical cycle. Here we show that such well-known features can be modified when a longer wavelength driving laser is used. From our simulations, we show that multiple shorter attosecond sub-bursts exist in the femtosecond pulse train within each half optical cycle and the duration of each sub-burst scales approximately as lambda-2 0 with the driving laser wavelength lambda 0. We show that such sub-bursts can be found using quantitative rescattering model for harmonics generated from a single atom, and their origin is due to the interference of the quantum orbits from first two returns of the recombining electron. We further show that such sub-bursts can be phase matched under proper laser focusing condition and the position of the gas cell, thus, such new features should be observable experimentally.