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We investigate lasing of a nitrogen gas induced by intense femtosecond laser pulses at around 400 nm. By examining both the self-induced and externally seeded forward emission spectra, we unambiguously identify the ${{\mathrm{N}}_{2}}^{+}$ lasing actions at 427.8 and 423.6 nm assigned respectively to the $B\phantom{\rule{0.16em}{0ex}}{}^{2}\mathrm{\ensuremath{\Sigma}}{{}_{u}}^{+}\ensuremath{-}X^{2}\mathrm{\ensuremath{\Sigma}}_{g}^{\phantom{\rule{0.28em}{0ex}}+}$ (0, 1) and (1, 2) emissions and show that the lasing mechanism is totally different from the lasing induced by near-infrared (800 nm) laser pulses, in which the population transfer from $X^{2}\mathrm{\ensuremath{\Sigma}}_{g}^{\phantom{\rule{0.28em}{0ex}}+}$ to $A^{2}\mathrm{\ensuremath{\Pi}}_{u}$ proceeds through the resonant $X^{2}\mathrm{\ensuremath{\Sigma}}_{g}^{\phantom{\rule{0.28em}{0ex}}+}\ensuremath{-}A^{2}\mathrm{\ensuremath{\Pi}}_{u}$ transition, facilitating the population inversion between the $B\phantom{\rule{0.16em}{0ex}}{}^{2}\mathrm{\ensuremath{\Sigma}}{{}_{u}}^{+}\ensuremath{-}X^{2}\mathrm{\ensuremath{\Sigma}}_{g}^{\phantom{\rule{0.28em}{0ex}}+}$ states [Phys. Rev. Lett. 123, 203201 (2019)]. We simulate the population distributions among the vibrational levels in the three lowest electronic states of ${{\mathrm{N}}_{2}}^{+}$ by the 400-nm laser pumping and find that the population is efficiently transferred between the $X^{2}\mathrm{\ensuremath{\Sigma}}_{g}^{\phantom{\rule{0.28em}{0ex}}+}$ state and the $B\phantom{\rule{0.16em}{0ex}}{}^{2}\mathrm{\ensuremath{\Sigma}}{{}_{u}}^{+}$ state by a Rabi oscillation combined with a Raman-type transition, leading to the population inversion so that the lasing occurs at the $B\phantom{\rule{0.16em}{0ex}}{}^{2}\mathrm{\ensuremath{\Sigma}}{{}_{u}}^{+}\ensuremath{-}X^{2}\mathrm{\ensuremath{\Sigma}}_{g}^{\phantom{\rule{0.28em}{0ex}}+}$ (0, 1) and (1, 2) emissions.

The authors determine the spin-orbit-splitting energies in the electronic ground states of Ar${}^{+}$, Kr${}^{+}$, and Kr${}^{2+}$ from the temporal evolution of wave packets generated by strong-field ionization of the neutral atoms and the singly charged ion, respectively. The results are in agreement with earlier measurements with significantly improved precision.

The lasing of ${\mathrm{N}}_{2}{}^{+}$ at 391 nm, originating from the population inversion between $X{\phantom{\rule{0.16em}{0ex}}}^{2}{\mathrm{\ensuremath{\Sigma}}}_{g}{}^{+}(v=0)$ and $B{\phantom{\rule{0.16em}{0ex}}}^{2}{\mathrm{\ensuremath{\Sigma}}}_{u}{}^{+}(v=0)$ achieved by the irradiation of a pair of few-cycle intense near-IR laser pulses in a pump-probe scheme, is investigated both experimentally and theoretically. The characteristic periodic intensity modulations recorded experimentally in both $P$- and $R$-branch emission lines are reproduced well by the theoretical simulation, in which the population transfer processes among the rovibrational levels of the three lowest electronic states, $X{\phantom{\rule{0.16em}{0ex}}}^{2}{\mathrm{\ensuremath{\Sigma}}}_{g}{}^{+}, A{\phantom{\rule{0.16em}{0ex}}}^{2}{\mathrm{\ensuremath{\Pi}}}_{u}$, and $B{\phantom{\rule{0.16em}{0ex}}}^{2}{\mathrm{\ensuremath{\Sigma}}}_{u}{}^{+}$, of ${\mathrm{N}}_{2}{}^{+}$ induced by pump and probe few-cycle intense laser pulses are calculated. Based on the results of the theoretical simulation, the periodic intensity modulations are ascribed to the difference between the rotational selection rules in the $A{\phantom{\rule{0.16em}{0ex}}}^{2}{\mathrm{\ensuremath{\Pi}}}_{u}\ensuremath{-}X{\phantom{\rule{0.16em}{0ex}}}^{2}{\mathrm{\ensuremath{\Sigma}}}_{g}{}^{+}$ coupling, which suppresses the rotational excitation in the $X{\phantom{\rule{0.16em}{0ex}}}^{2}{\mathrm{\ensuremath{\Sigma}}}_{g}{}^{+}(0)\phantom{\rule{0.28em}{0ex}}\text{state}$, and those in the $B{\phantom{\rule{0.16em}{0ex}}}^{2}{\mathrm{\ensuremath{\Sigma}}}_{u}{}^{+}\ensuremath{-}X{\phantom{\rule{0.16em}{0ex}}}^{2}{\mathrm{\ensuremath{\Sigma}}}_{g}{}^{+}$ coupling, which enhances the rotational excitation in the $B{\phantom{\rule{0.16em}{0ex}}}^{2}{\mathrm{\ensuremath{\Sigma}}}_{u}{}^{+}$(0) state.

We apply a modified version of the multistate contracted variational quantum eigensolver method to calculate vibrational eigenstates of ${\mathrm{CO}}_{2}$ on a quantum computer. A two-mode model of ${\mathrm{CO}}_{2}$ is employed, and the vibrational wave function is expanded using three harmonic-oscillator basis functions for each mode. The wave functions are mapped to four qubits by a compact mapping method. The Hamiltonian matrix elements are evaluated on a simulator including noise and on a quantum computer available at IBM Quantum, while the Hamiltonian matrix is diagonalized on a classical computer. We propose an error mitigation method by which the shift of the numerical values of the matrix elements originating from the noise can be corrected, and examine the dependence of the statistical uncertainties on the number of executions of each quantum circuit. We find that, at about $8\ifmmode\times\else\texttimes\fi{}{10}^{6}$ executions, the energy eigenvalues of the Fermi resonance states in ${\mathrm{CO}}_{2}$ can be obtained with an uncertainty within 1 ${\mathrm{cm}}^{\ensuremath{-}1}$.

We investigate the photoionization of ${\mathrm{H}}_{2}$ by an attosecond pulse train using reduced density matrices and reveal that the phase of the photoelectron introduces a time delay in the coherent vibrational motion of ${\mathrm{H}}_{2}^{+}$. We show that, even when the ionization laser pulse is Fourier limited, the reduced density matrix of ${\mathrm{H}}_{2}^{+}$ contains an intrinsic phase ascribed to the phase of the photoelectron wave function and that the intrinsic phase can be extracted by pump-probe measurements as long as the pump-probe time delay is measured with precision of the order of tens of attoseconds.

We make a theoretical investigation of photoionization of an ${\mathrm{H}}_{2}$ molecule, induced by the irradiation of an ultrashort extreme ultraviolet (XUV) laser pulse. We consider a system composed of a photoelectron ejected from ${\mathrm{H}}_{2}$ and the resultant ${{\mathrm{H}}_{2}}^{+}$ as a bipartite system. In order to clarify how the interparticle correlations among two electrons and two protons in ${\mathrm{H}}_{2}$ are reflected to the bipartite system, we examine the entanglement between the photoelectron and the vibrational states of ${{\mathrm{H}}_{2}}^{+}$ as well as the coherence in the vibrational states of ${{\mathrm{H}}_{2}}^{+}$ by simulating the photoionization process of one-dimensional ${\mathrm{H}}_{2}$. In the simulation, we solve a time-dependent Schr\"odinger equation using a symmetry-adapted grid method. On the basis of the simulations with ten different sets of three parameters characterizing an ultrashort XUV laser pulse, i.e., the pulse duration, the wavelength, and the peak intensity, we show that the extent of the entanglement depends sensitively on the coherence in the vibrational states of ${{\mathrm{H}}_{2}}^{+}$.

We apply the extended multiconfiguration time-dependent Hartree-Fock method to the simulation of a hydrogen molecular ion exposed to an intense laser pulse. By comparing the results obtained by this method with the results obtained by a method in which the time-dependent Schr\"odinger equation is solved directly on a three-dimensional grid, we find that the results obtained by these two methods are in good agreement with each other when the number of time-dependent expansion terms exceeds 8. We further compare the results with those obtained by the conventional two-state Born-Oppenheimer approximation. In order to interpret the resultant time-dependent wave functions, we decompose the total wave function into the natural electronic and protonic orbitals that diagonalize the single-particle density matrices and find that the pair of electronic and protonic natural orbitals carrying the largest population describes the vibrational excitation, while the pair carrying the second largest population describes the dissociation into $\text{H}+{\mathrm{H}}^{+}$. We also examine the time-dependent motion of the protons in ${\mathrm{H}}_{2}^{+}$ in terms of the time-dependent adiabatic potential-energy curves, which are defined as the instantaneous eigenvalues of the Hamiltonian matrix governing the time-dependent motion of the protonic orbitals. We show that two potential minima are formed on the lowest-energy adiabatic potential-energy curve and that the nuclear wave packet localized in the inner minimum corresponds to the bound vibrational motion, while the nuclear wave packet localized in the outer minimum corresponds to the dissociation.

We derive a variation equation for a time-dependent effective potential that is local both in time and in space and show that this potential generates and propagates spin orbitals with which a many-particle, time-dependent, multiconfigurational wave function $\mathrm{\ensuremath{\Psi}}(t)$ is constructed. Within this approach, the wave function and the effective potential are determined simultaneously in a self-consistent manner both in time-independent and in time-dependent cases. We also derive an equation that determines a real-valued effective potential and show that the equation establishes a relation among the first-order and second-order reduced density matrices and the electron repulsion integrals in the spin-orbital representation. By introducing the first-order density equation, we show that the variation equation for the effective potential can be simplified for an exact wave function. We also show that we can derive an effective potential with which a ground-state wave function that fulfills the Brillouin-Brueckner condition is constructed and that we can derive the effective potential proposed by Slater, with which a ground-state wave function represented by the multiconfiguration expansion is calculated, when an additional constraint is imposed on the varitation equation.

We align nonadiabatically an ensemble of ${\mathrm{N}}_{2}$ in air, and irradiate the ensemble with linearly polarized intense few-cycle laser pulses to generate population-inverted ${\mathrm{N}}_{2}{}^{+}$ ions. By probing the self-seeded lasing signals of ${\mathrm{N}}_{2}{}^{+}$ at 391 nm, we show that the ultrafast population inversion in ${\mathrm{N}}_{2}{}^{+}$ between the electronic ground $X\phantom{\rule{0.16em}{0ex}}^{2}\mathrm{\ensuremath{\Sigma}}_{\mathrm{g}}$ state and the electronically excited $B\phantom{\rule{0.16em}{0ex}}^{2}\mathrm{\ensuremath{\Sigma}}_{\mathrm{u}}$ state is sensitively influenced by the extent of the alignment of ${\mathrm{N}}_{2}$ with respect to the polarization direction of the few-cycle laser field. The observed alignment dependence of the air lasing is reproduced well by numerical calculations performed based on a theoretical model in which the population transfer to the $B\phantom{\rule{0.16em}{0ex}}^{2}\mathrm{\ensuremath{\Sigma}}_{\mathrm{u}}$ state from the $X\phantom{\rule{0.16em}{0ex}}^{2}\mathrm{\ensuremath{\Sigma}}_{\mathrm{g}}$ state of ${\mathrm{N}}_{2}{}^{+}$ in the ultrashort laser field is mediated by the $A\phantom{\rule{0.16em}{0ex}}^{2}\mathrm{\ensuremath{\Pi}}_{\mathrm{u}}$ state. Our findings show that the intensity of the air lasing can be manipulated precisely by the timing between the laser pulses inducing the alignment of ${\mathrm{N}}_{2}$ and the laser pulse ionizing ${\mathrm{N}}_{2}$ into ${\mathrm{N}}_{2}{}^{+}$ as well as by the difference in the laser polarization directions of these laser pulses.

The angle-resolved photoelectron spectra of Ar are recorded using intense circularly polarized near-infrared few-cycle laser pulses, and the effect of the depletion of Ar atoms by the ionization and the effect of the Coulombic potential are examined by the classical trajectory Monte Carlo simulations. On the basis of the comparison between the experimental and theoretical photoelectron spectra, a procedure for estimating the absolute carrier-envelope phase (CEP) of the few-cycle laser pulses interacting with atoms and molecules is proposed. It is confirmed that the absolute CEP can securely be estimated without any numerical calculations once the angular distribution of the yield of photoelectrons having the kinetic energy larger than 30 eV is measured with the peak laser intensity in the range between $1\ifmmode\times\else\texttimes\fi{}{10}^{14}$ and $5\ifmmode\times\else\texttimes\fi{}{10}^{14}\phantom{\rule{0.16em}{0ex}}\mathrm{W}/\mathrm{c}{\mathrm{m}}^{2}$.

A scheme for achieving high temporal resolution in gas electron diffraction is proposed, in which time-dependent electron diffraction patterns can be obtained from energy-resolved angular distributions of electrons scattered by molecules in dynamical processes under the presence of a single-cycle THz-wave pulse. Derived formulae of the differential cross section and numerical simulations of electron signals scattered by Ar atoms and $\mathrm{C}{\mathrm{l}}_{2}$ molecules show that the temporal resolution of the proposed method can be $l10\phantom{\rule{0.16em}{0ex}}\mathrm{fs}$ in the pump-probe measurement without scanning the time delay.

Photoinduced dynamics of a weakly bound triatomic molecule $\mathrm{He}{{\mathrm{H}}_{2}}^{+}$ exposed to electromagnetic radiation is investigated by time-dependent quantum wave-packet propagation. Adopting a two-dimensional linear H-H-He model, the three lowest-lying potential energy surfaces (PESs) and corresponding dipole moment surfaces are constructed. One of the two characteristic excited PESs of $\mathrm{He}{{\mathrm{H}}_{2}}^{+}$ leads to the charge-transfer reaction ${{\mathrm{H}}_{2}}^{+}+\mathrm{He}\ensuremath{\rightarrow}{\mathrm{H}}_{2}+\mathrm{H}{\mathrm{e}}^{+}$ and the other corresponds to the first excited state of ${{\mathrm{H}}_{2}}^{+}$ perturbed by the presence of He. When $\mathrm{He}{{\mathrm{H}}_{2}}^{+}$ is exposed to a femtosecond intense ultraviolet light pulse ($I=4\ifmmode\times\else\texttimes\fi{}{10}^{14}\phantom{\rule{4pt}{0ex}}\mathrm{W}\phantom{\rule{0.16em}{0ex}}\mathrm{c}{\mathrm{m}}^{\ensuremath{-}2}, \ensuremath{\lambda}=400\phantom{\rule{0.16em}{0ex}}\mathrm{nm}$), both of the two excited PESs are found to be coupled with the light field and a variety of reaction pathways become opened so that HeH, $\mathrm{He}{\mathrm{H}}^{+}, {\mathrm{H}}_{2},\phantom{\rule{0.16em}{0ex}}{{\mathrm{H}}_{2}}^{+},\phantom{\rule{0.16em}{0ex}}\mathrm{H},\phantom{\rule{0.16em}{0ex}}{\mathrm{H}}^{+}$, He, and $\mathrm{H}{\mathrm{e}}^{+}$ are produced. Simulations also show that the anharmonic coupling between the two stretching vibrational modes in $\mathrm{He}{{\mathrm{H}}_{2}}^{+}$ leads to the stabilization of the ${{\mathrm{H}}_{2}}^{+}$ moiety against the decomposition into $\mathrm{H}+{\mathrm{H}}^{+}$ compared with bare ${{\mathrm{H}}_{2}}^{+}$. The theoretical findings of the formation of $\mathrm{He}{\mathrm{H}}^{+}$ composed of the most abundant elements in the universe are also discussed in view of the theoretical modeling of the chemical reactions proceeding in the primordial gas and in the interstellar medium.

We experimentally investigate the ionization mechanism behind the formation of remarkably high charge states observed in the laser-pulse-induced fragmentation of different hydrocarbon molecules by Roither et al. [Phys. Rev. Lett. 106, 163001 (2011)], who suggested enhanced ionization occurring at multiple C-H bonds as the underlying ionization mechanism. Using multiparticle coincidence momentum imaging we measure the yield of multiply charged fragmenting ethylene and acetylene molecules at several intensities and pulse durations ranging from the few-cycle regime to 25 fs. We observe, at constant intensity, a strong increase of the proton energy with increasing laser pulse duration. It is shown that this is caused by a strong increase in the yield of highly charged parent molecular ions with pulse duration. Based on experimental evidence we explain this increase by the necessary population of precursor states in the parent ion that feature fast C-H stretch dynamics to the critical internuclear distance, where efficient ionization via enhanced ionization takes place. For increasing pulse duration these precursor ionic states are more efficiently populated, which leads in turn to a higher enhanced-ionization probability for longer pulses. Our work provides experimental evidence for the existence of a multiple-bond version of enhanced ionization in polyatomic molecules.

The ionization of a model acetylene molecule (C${}_{2}$H${}_{2}$) by an intense laser pulse is studied by numerically solving the time-dependent Hartree-Fock equations. It is shown that when the C--H bond is stretched to twice the value of the equilibrium internuclear distance, the ionization probability is strongly enhanced. The physical mechanism is identified to be similar to the enhanced ionization found previously in H${}_{2}^{+}$, with the two HOMOs in acetylene playing the same role as the charge resonance states $1{\ensuremath{\sigma}}_{g}$ and $1{\ensuremath{\sigma}}_{u}$ in H${}_{2}^{+}$. Electrons are ejected in a two-step process. First, the electron density is transferred to one of the peripheral H atom sites, and then it is ejected from there by tunneling. The same process is effective also in C${}_{2}$H${}_{2}$${}^{2+}$. The mechanism is further clarified by employing both a simplified two-state model and the single-active-orbital approximation. In the enhancement of the ionization of C${}_{2}$H${}_{2}$, the elongation of the C--H distance plays a decisive role, while the variation of the C--C distance gives only a secondary contribution. In addition to the two highest occupied molecular orbitals, electrons in the third highest molecular orbital are also found to be ejected efficiently. The role of the third highest molecular orbital in the ionization dynamics is investigated by introducing projection operators.

Acetylene (C${}_{2}$H${}_{2}$), described by a one-dimensional model, is shown to be extremely efficiently ionized by an intense laser field when the two C-H distances are symmetrically stretched to twice the equilibrium distance. Up to six electrons are ejected from the three highest occupied molecular orbitals by tunneling ionization through a reduced potential barrier via temporal localization of the electron density at either of the two proton sites. The third highest occupied molecular orbital, which is initially localized in the area around the two C atoms, is found to act as an electron reservoir, through which the electron density is transferred to the proton sites. This electron transfer mechanism is considered to be universal and can be applied to interpret enhanced ionization found in a variety of hydrocarbon molecules.

High-order harmonic radiation is available to investigate ultrafast nonlinear optical phenomena, such as two-photon absorption process, in the vacuum and extreme ultraviolet wavelength region. We have determined the sequential two-photon dissociative ionization pathways of D2 with the simultaneous irradiation of multiple order harmonics of a Ti:sapphire laser in the visible-vacuum ultraviolet region with the aid of both an interferometric autocorrelation measurement and a Fourier-transform spectroscopy. By analyzing the interferometric autocorrelation signals appearing in the measured momentum distribution of D + , we were able to decompose the measured momentum distribution into three momentum distribution images representing the three distinct dissociation pathways, which are sequentially two-photon excitation processes of D2. \({\mathrm{D}}_{2}^{+}\) is prepared in the electronic ground state of \({\mathrm{D}}_{2}^{+}\), and then excited to the first excited state, leading to the dissociation into D + and D.

We report the direct observation of phase locking between adjacent pulses in an attosecond pulse train (APT) via interferometric autocorrelation (IAC). In this measurement, the Coulomb explosion of ${\mathrm{N}}_{2}$ caused by two-photon absorption is utilized as correlated signals between two replicas of the APT that are the outcome of the spatial division of the APT in the interferometer. The analysis of IAC by the spatial division of the APT is consistent with the experimental trace of the IAC, and yields the duration of the pulse in the APT of $320\phantom{\rule{0.3em}{0ex}}\text{attoseconds}$, which corresponds to a $1.3\phantom{\rule{0.3em}{0ex}}\text{cycle}$ period of the carrier frequency of the harmonic field.