Multielectron tunneling ionization creates ionic coherence crucial for lasing and driving electron motion in molecules. While tunneling is well understood as a single active electron process, less emphasis has been placed on theoretical descriptions of bound electrons during tunneling. This work systematically investigates multielectron tunneling ionization based on the strong field approximation, establishing a theoretical foundation and demonstrating the equivalence of wave function and density matrix approaches for subcycle ionic dynamics. An accurate subcycle nonadiabatic ionization rate is also derived and incorporated into the theory to improve its quantitative accuracy. Applying the theory to N$_{2}$ and CO$_{2}$, this work showcases how an intense laser field can induce ionic coherence in molecules as observed in previous experiments. These findings encourage future investigations into multielectron tunneling ionization and its applications in lasing and in controlling chemical reactions.

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.

Tunnel ionization-assisted laser-induced electron diffraction (TI-LIED) has been successfully demonstrated as an effective technique for distinguishing structural isomers such as butane and isobutane [C.-H. Yuen et al. (unpublished)]. The inclusion of the tunnel ionization rate becomes increasingly important for larger molecules, where it significantly influences the scattering signal. In this work we begin by revisiting prior studies on two stereoisomers, 1,2-dichloroethylene (C2H2Cl2) and 2-butene (C4H8), which were previously shown to be distinguishable through their high-harmonic generation (HHG) spectra. We show that TI-LIED amplifies the scattering signal by different amounts across these isomers, producing strong contrast that peaks at backscattering, and offering a simpler, more direct alternative to HHG-based methods. Next, we demonstrate that TI-LIED has broader applicability beyond the identification of isomers. To illustrate this, we apply the method to two additional scenarios. The first examines structurally similar, but nonisomeric, molecules. An example used here is acetylene and diacetylene. TI-LIED successfully differentiates these molecules, highlighting its potential for resolving closely related molecular structures. The second case features dynamic molecules. We use the symmetric N-N stretching mode of N2O4 as an example. As the N-N bond length (RNN) varies, the backscattering differential cross section oscillates strongly with RNN with the inclusion of TI rate, clearly reflecting the underlying structural change. With the progression of molecular imaging toward more complex species, TI-LIED is expected to become an increasingly important tool for structural analysis.

Tunneling ionization followed by strong-field excitation leads to important ultrafast phenomena such as charge migration and lasing. Recent theoretical developments suggest that the population of the ionic excited state can be greatly enhanced due to the complex interplay between tunneling and excitation. In this Letter, using an adiabatic approach for both tunneling and excitation, semi-analytical solutions are derived for the population and coherence of a two-level ionic system. This approach removes the strong-field dressing, revealing novel sub-half-cycle processes for excited state population and coherence buildup. It predicts that the excited state population is enhanced by an order of magnitude, independent of the laser wavelength, while coherence amplitude can be boosted by over four orders of magnitude for a multi-cycle pulse. For a single-cycle pulse, it suggests that coherence amplitude decreases rapidly as the wavelength increases. This work introduces a novel framework for generating and controlling the electronic excited state and coherence using intense laser pulses, with applications in strong-field control of chemistry and lasing.

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.

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.

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.

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.

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.

Understanding the dissociative electron attachment (DEA) in low-temperature ammonia plasma is crucial for many technological applications, in particular, for alternative energy sources. However, theoretical modeling of this process has been challenging due to the complex interplay of electronic motion and multidimensional nuclear dynamics. This Letter presents a theoretical approach to investigate the process, applying it to the breakup of the NH3 molecule by low-energy electrons. The potential energy surface of the NH3- 5.5 eV resonant state is computed to elucidate the mechanism of the dissociative process. The cross section of DEA via the 5.5 eV resonance is then calculated for both NH3 and ND3. The positions of the peaks in both cross sections and the ratio between them are in excellent agreement with previous experiments. Our findings suggest that the developed theoretical model accurately describes the DEA process and could serve as a useful tool for providing DEA cross sections for other molecules to model low-temperature plasma.

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.

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.

Probing vibronic coherence in molecules has been a central topic in ultrafast science, as it is an essential prerequisite to monitoring electronic motion. While experiments have demonstrated that attosecond transient absorption spectroscopy (ATAS) can probe the vibronic coherence in a few molecules, its robustness remains largely unexplored. In this Letter, we develop a comprehensive theory for ATAS which accounts for the orientation dependence of the density matrix of a pumped molecule. We apply our theory to N$_2^+$ formed by multiorbital tunnel ionization under a few-cycle intense near-infrared laser pulse. The simulated x-ray absorption spectrum shows clear signatures of the vibronic coherence between the $A^2\Pi_u$ and $B^2\Sigma_u^+$ states of N$_2^+$, which was predicted to be absent by a previous theory. We further define a coherence contrast factor to quantify the robustness of ATAS. This work advances the theoretical foundation of ATAS and paves the way for monitoring electronic motion in generic molecules.

A density matrix approach for sequential double ionization (DM-SDI) of molecules has been developed recently and was applied to the N2 molecule [Yuen and Lin, Phys. Rev. A 106, 023120 (2022)]. In this article, we extended the DM-SDI model to O2, which is a more complicated system to model than N2, due to its electronic structures and spin-orbit and laser couplings in the manifold of doubly charged states. We obtained a good agreement on the kinetic energy release spectrum of O+ + O+ from previous experiments. Thanks to the low computational cost of the model, we explored the mechanism behind the ionization and dissociation dynamics as well as the effects of lasers on the spectrum. This work will pave the way to model sequential dissociative double ionization of larger molecules and to probe molecular dynamics by measuring kinetic energy release spectra from this process.

Intense femtosecond infrared (IR) laser pulses have been used in recent years to study the breakup dynamics of molecules. However, observables such as kinetic energy release and branching ratios of molecular fragments are often difficult to predict by theory, making information of the molecular dynamics difficult to retrieve. In this work, we develop a simple model for sequential double ionization of molecules based on a density-matrix approach. The model describes tunneling ionization of the neutral and the ion as well as laser couplings between the ionic states simultaneously. Population of different doubly charged states can be obtained at a low computational cost. We applied our model to N-2 and obtained a good agreement on the kinetic energy release spectrum with a previous experiment. This theoretical development could open up the opportunities to use intense short IR laser pulses with coincidence measurement to probe molecular dynamics.

We rigorously calculate the conservative gradient force (GF) and the non-conservative scattering force (SF) associated with the optical tweezers (the single beam optical trap). A wide range of parameters are considered, with particle size ranging from the Rayleigh to Mie regime (radius ∼3 µm), dielectric constant ranging from metallic (large and negative) to high dielectrics (large and positive), numerical aperture (NA) ranging from 0.5 to 1.33, and different polarizations. The trap depth associated with GF can reach 123 and 168 kBT per mW for a 0.5 µm-radius polystyrene particle illuminated by a 1064 nm Gaussian beam with NA = 0.9 and 1.3, respectively. This indicates that unless at a low beam power or with a small NA, the Brownian fluctuations do not play a role in the stability. The transverse GF orthogonal to beam propagation always dominates over the transverse SF. While the longitudinal SF can be larger than the longitudinal GF when the scattering is strong, the NA is small, or when absorption is present, optical trapping under these conditions is difficult. Generally speaking, absorption reduces GF and enhances SF, while increasing a dielectric constant enhances GF slightly but boosts SF significantly owing to stronger scattering. These results verify previous experimental observations and explain why optical tweezers are so robust across such a wide range of conditions. Our quantitative calculations will also provide a guide to future studies.

The process of electron attachment to the NO2 molecule is investigated theoretically using an approach based on a study by O’Malley (1966 Phys. Rev. 150 14). The approach combines the normal mode approximation for representation of vibrational dynamics of NO2 and one-dimensional treatment, along each normal mode, of the attachment process as in O’Malley’s theory, such that only a modest computational effort is required to compute the attachment cross section. Taking into account the survival probability of the formed resonant state of NO2− , the cross section for dissociative electron attachment to NO2 is also estimated. To compare with available experimental data, the theoretical cross section is convoluted with energy distribution of NO2–e− collisions with uncertainties reported in experimental studies. Peak values of the convoluted theoretical cross section are found to be about a factor of 2–10 larger than the experimental results.

The authors present a computational analysis of dissociative recombination of CH${}^{+}$, in which both direct and indirect mechanisms are included. Good agreement with experiments is found in a wide regime while an explanation for disagreement was provided at lower energies. The theoretical method used in this study could be applicable in a wide range of diatomic cations.