Molecules In Intense Laser Fields Research Articles

Breakdown of one-to-one correspondence between the photoelectron emission angle and the tunneling instant in the attoclock scheme

Attoclock is a promising chronoscopy of the ultrafast dynamics of atoms and molecules in intense laser fields. The attoclock procedure is established based on the one-to-one correspondence between the photoelectron emission angle and the tunneling instant at each photoelectron kinetic energy for ionization of atoms and molecules subject to elliptically polarized strong laser fields. In this work, our joint theoretical and experimental study demonstrates that this correspondence could be broken down for photoelectrons emitted in a direction close to the minimum yield. Two trajectories with different tunneling instants and different initial velocities are found to correspond to a specific final momentum of the photoelectron in this direction, and a multi-peak structure appears in the photoelectron kinetic energy spectrum that can be attributed to interference between these two trajectories. Our work is essential for a deeper understanding and further development of the attoclock scheme.

Minimum structure of high-order harmonic spectrum from molecular multi-orbital effects involving inner-shell orbitals.

The spectral features of high-order harmonic spectra can provide rich information for probing the structure and dynamics of molecules in intense laser fields. We theoretically study the high harmonic spectrum with the laser polarization direction perpendicular to the N2O molecule and find a minimum structure in the plateau region of the harmonic spectrum. Through analyzing the time-dependent survival probability of different electronic orbitals and the time-dependent wave packet evolution, it is found that this minimum position is caused by the harmonic interference of HOMO a, HOMO-1, and HOMO-3 a orbitals. Moreover, this interference minimum is discovered over a wide frequency range of 0.087a.u. to 0.093a.u., as well as a range of driving laser intensities with peak amplitudes between 0.056 a.u. and 0.059 a.u.. This study sheds light on the multi-electron effects and ultrafast dynamics of inner-shell electrons in intense laser pulses, which are crucial for understanding and controlling chemical reactions in molecules.

PyStructureFactor: A Python code for the molecular structure factor in tunneling ionization rates

Tunneling ionization is at the core of strong-field and attosecond science. In this paper, we present PyStructureFactor — a general Python code towards the calculation of the structure factor in the tunneling ionization rate of common molecules under intense laser fields. The numerical implementation is based on the well-developed weak-field asymptotic theory in the integral representation. The information of the electronic structure of the molecules is obtained via the PySCF quantum chemistry package. PyStructureFactor is a general computational framework that can be utilized to compute the molecular structure factor of various types of molecules, including polar and nonpolar diatomic molecules, degenerate molecules, and open-shell molecules. Examples are given that are benchmarked against known results with good agreements. The present PyStructureFactor is implemented in an efficient manner and is easily applicable towards larger molecules. Program summaryProgram title: PyStructureFactorCPC Library link to program files:https://doi.org/10.17632/td88mhw2sg.1Developer's repository link:https://github.com/TheStarAlight/PyStructureFactorLicensing provisions: Apache-2.0Programming language: Python 3Nature of problem: The structure factor of a molecule in intense laser fields determines its orientation-dependent tunneling ionization rate, which is crucial for the studies of ultrafast molecular dynamics and its control. However, the strong-field community lacks an open-source code to calculate the molecular structure factor, and can only resort to known results of a few molecules.Solution method: We developed the PyStructureFactor program with the structure factor of arbitrary molecules calculated using the weak-field asymptotic theory in the integral representation. The underlying electronic structure necessary for the calculation is obtained using the PySCF quantum chemistry package.Additional comments including restrictions and unusual features: The accuracy of the molecular structure factor calculated by PyStructureFactor is restricted by the level of precision of the electronic structure information extracted from the PySCF package.The running time depends on the size of the molecule, the basis set of the calculation, the level of precision of the electronic structure calculations, and other parameters passed to the program. The example in Fig. 2 took 1.2 seconds to finish on an AMD Ryzen 9 7950X CPU on the WSL Ubuntu 22.04 LTS.

Influence of ac Stark shift on below-threshold harmonic generation of H molecular ions in intense laser fields

The effects of laser-induced ac Stark shift on the high-order harmonic generation below the ionization threshold of H molecular ions are investigated. The results show that several sub-peak harmonics generated in the vicinity of odd harmonics are clearly observed. Combined with the synchrosqueezing transform of the quantum time-frequency spectrum and a two-state model, we confirm that the transition between the first excited state related to ac Stark-shift and the ground state contributes to the sub-peak harmonics generation. In addition, we find some fine oscillatory structures of the sub-peak harmonic due to spectral interference. The sub-peak harmonics generation and spectral oscillations can be controlled by the laser intensity and the pulse duration. Our study provides a new alternative way to measure the energy difference of ac Stark shift between the excited state and the ground state of atoms and molecules in intense laser fields.

Generation of ellipticity-tunable isolated attosecond pulses from diatomic molecules in intense laser fields

We theoretically investigate the high-order harmonic generation (HHG) and the isolated attosecond pulse (IAP) with tunable ellipticity from the aligned molecule. It is found that the ellipticity of harmonic depends on the internuclear distance R. Further analysis presents that the nonzero ellipticity of harmonic generated at R=6a.u. is attributed to the 2pσu state of H2+. The 2pσu state with nonvanishing angular momentum originates from a resonant transition from the 1sσg state induced by the fundamental pulse. With specific intensity of the orthogonally polarized two-color (OTC) laser fields, an IAP with high ellipticity can be obtained. To further illustrate the origin of the high ellipticity, we present the electron trajectories and electron currents induced by the electron wavepackets of H2+, which shows a clear picture of the dynamic process of HHG. Moreover, the polarization of the IAP varies from left to right elliptical polarization by synthesizing the harmonic spectrum with different orders. Such an IAP may serve as a potential tool for probing and manipulating the ultrafast magnetic and chiral dynamics.

Photoionization and Photofragmentation Dynamics of I2 in Intense Laser Fields: A Velocity-Map Imaging Study.

The photoionization and photofragmentation dynamics of I2 in intense femtosecond near-infrared laser fields were studied using velocity-map imaging of cations, electrons, and anions. A series of photofragmentation pathways originating from different cationic electronic states were observed following single ionization, leading to I+ fragments with distinct kinetic energies, which could not be resolved in previous studies. Photoelectron spectra indicate that these high-lying dissociative states are primarily produced through nonresonant ionization from several molecular orbitals (MO) of the neutral. The photoelectron spectra also show clear signatures of resonant ionization pathways (Freeman resonances) to low-lying bound ionic states via Rydberg states of the neutral moiety. To investigate the role of these Rydberg states further, we imaged anionic products (I-) formed through ion-pair dissociations of neutral molecules excited to these Rydberg states by the intense femtosecond laser pulse. Collectively, these results shed significant new light on the complex dynamics of I2 molecules in intense laser fields and on the important role of neutral Rydberg states in a full description of strong-field phenomena in molecules.

Channel Coupling Dynamics of Deep-Lying Orbitals in Molecular High-Harmonic Generation.

Investigation on structures in the high-harmonic spectrum has provided profuse information of molecular structure and dynamics in intense laser fields, based on which techniques of molecular ultrafast dynamics imaging have been developed. Combining abinitio calculations and experimental measurements on the high-harmonic spectrum of the CO_{2} molecule, we find a novel dip structure in the low-energy region of the harmonic spectrum which is identified as fingerprints of participation of deeper-lying molecular orbitals in the process and decodes the underlying attosecond multichannel coupling dynamics. Our work sheds new light on the ultrafast dynamics of molecules in intense laser fields.

Recollision of excited electron in below-threshold nonsequential double ionization

Recollision is the most important post-tunneling process in strong-field physics, but so far has been restricted to interaction between the first ionized electron and the residual ion in nonsequential double ionization. Here we identify the role of recollision of the second ionized electron in the below-threshold nonsequential double ionization process by introducing a Coulomb-corrected quantum-trajectories method. We will reproduce the experimentally observed cross-shaped and anti-correlated patterns in correlated two-electron momentum distributions, and the transition between them. Both the cross-shaped and anti-correlated patterns are attributed to recolliding trajectories of the second electron. The effect of recollision of the second electron is significantly enhanced by the stronger Coulomb potential of the higher valence residual ion, and is further strengthened by the recapture process of the second electron. Our work paves a potential way to image ultrafast dynamics of atoms and molecules in intense laser field.

Tunneling delay time in strong field ionization of atomic Ar

“Attoclock” provides a promising experimental scheme to explore the timing of tunnel ionization of atoms and molecules in intense laser fields. In this work, we perform a systematical investigation of tunneling delay time in strong field ionization of atomic Ar, based on the “attoclock” experimental scheme. Experimentally, the laser intensity dependence of the photoelectron momentum distributions of Ar subject to strong elliptically polarized laser fields at 800 nm has been measured. Theoretically, a dedicated semiclassical model, in which the Coulomb potential effect, the nonadiabatic effect, the Stark effect, the multielectron screening and polarization effect have been well considered, is employed to simulate the ionization dynamics of Ar. By comparing the experimental and simulated results, an upper limit of 10 attoseconds for the tunneling delay time of Ar has been derived for the laser intensity ranges explored in this work. In addition, the influence of various physical effects on the extracted tunneling delay time, in the context of semiclassical model, has been analyzed. It is demonstrated that, under otherwise identical conditions, consideration of multielectron screening effect will give rise to the least change of the extracted tunneling delay time. In contrast, consideration of nonadiabatic effect will lead to the most significant change of the extracted tunneling delay time.

Rabi-flopping signatures in below-threshold harmonic generation from the stretched H2 and N2 molecules in intense laser fields

We theoretically study the spectral and temporal fine subpeak structures in the below-threshold harmonic (BTH) spectra of the stretched H2 and N2 molecules by solving the one-electron time-dependent Schrödinger equation (TDSE) in conjunction with the wavelet time-frequency analysis. We identify such fine subpeaks come from the Rabi-flopping between the ground state and the first excited state using the simple two-state model. We also confirm that these subpeak structures in BTH spectra are common for molecules at large internuclear distances if two molecular states are strongly coupled. Furthermore, the spacing between the adjacent subpeaks in BTH spectra can be determined approximately by analyzing the induced dipole moment in the time domain.

Exploration of electron vortices in the photoionization of diatomic molecules in intense laser fields

Based on the approach within the single-electron approximation (SEA) frame, we numerically solve the two-dimensional (2D) time-dependent Schrdinger equation of N2 molecules under co-rotating and counter-rotating circularly polarized attosecond pulses. The vortex structure appears in counter-rotating circularly laser fields rather than the co-rotating case. The calculated vortex structures corresponding to the photoionization are found to be sensitive to the time delays T d of the two pulses, laser ellipticities and carrier envelope phases (CEPs). As the ellipticity increases to 1, the momentum distribution rotates and a vortex structure appears, and the interference is proved to play an important role in momentum distribution. The vortex structures also rotate clockwisely as the relative CEPs increase. The arms of the vortex structure become longer and thinner with the increasing T d . All these phenomena can be well understood by the attosecond perturbation ionization theory and the interference effect. Our findings clarify the applicability of the SEA model of diatomic molecules in attosecond extreme-ultraviolet fields.

Spatial distribution on high-order-harmonic generation of an H2 + molecule in intense laser fields

SynopsisHigh-order-harmonic generation (HHG) for the H2 + molecule in a 3-fs, 800-nm few-cycle Gaussian laser pulse is investigated by solving the time-dependent Schrödinger equation. The spatial distribution on HHG is demonstrated and the results present the recombination process of the electron with the two nuclei. And there is little possibility of the recombination of the electron with the nuclei around the origin z = 0 a.u. and equilibrium internuclear positions z = ±1.3 a.u.. The electron-nuclear wave packet and ionization probability are investigated to explain the physical mechanism.

Time-dependent effective potential for the ultrafast correlated electron dynamics of molecules in intense laser fields: Application to anisotropic ionization of CO

By using the multiconfiguration time-dependent (TD) Hartree-Fock (MCTDHF) method, we simulated the multielectron dynamics of a CO molecule irradiated by near-IR two-cycle pulses with different carrier envelope phases. The ionization rate calculated is higher when the laser electric field ε (t) points from the nucleus C to O than the opposite case, in agreement with the results of two-color ionization experiments. The mechanism of anisotropic tunnel ionization in CO was examined by converting the obtained multielectron dynamics to the representation in terms of TD natural orbitals {ϕj (t)}. Within the framework of MCTDHF, we derived the unitary equations of motion for {ϕj (t)}. From the derived equations, we defined the TD effective potentials that govern the dynamics of {ϕj (t)}. In for the 5σ HOMO, a narrow hump that originates from two-body electron-electron repulsion is formed on the top of the field-induced distorted barrier near the nucleus C when ε (t) points from C to O, which is responsible for the directional anisotropy of tunnel ionization. For 4σ HOMO-2, a high barrier to suppress ionization is formed in when ε (t) points from C to O, in correlation with the electron-electron interaction with a 5σ electron on route to ionization. For the opposite phase, becomes barrierless, which enhances high-harmonic generation through ϕ 4σ(t).

Nondipole strong-field approximation for spatially structured laser fields

The strong-field approximation (SFA) is widely used to theoretically describe the ionization of atoms and molecules in intense laser fields. We here propose an extension of the SFA to incorporate nondipole contributions in the interaction between the photoelectron and the driving laser field. To this end, we derive Volkov-type continuum wave functions of an electron propagating in a laser field of arbitrary spatial dependence. Based on previous work by L. Rosenberg and F. Zhou [Phys. Rev. A 47, 2146 (1993)], we show how to construct such Volkov-type solutions to the Schr\odinger equation for an electron in a vector potential that can be written as an integral superposition of plane waves. These solutions are therefore not restricted to plane waves but are also appropriate to deal with more complex laser fields like twisted Bessel or Laguerre-Gaussian beams, where the magnetic field plays an important role. As an example, we compute photoelectron spectra in the above-threshold ionization of atoms with a single-mode plane-wave laser field of midinfrared wavelength. Especially, we demonstrate how peak offsets in the ${p}_{z}$ direction can be extracted that result from the nondipole nature of the interaction. Here, we find good agreement with previous theoretical and experimental studies for circular polarization and discuss differences for linear polarization.

Ab initio molecular dynamics study of the reactions of allene cation induced by intense 7 micron laser pulses

ABSTRACTThe isomerisation and fragmentation of allene cation (H2C=C=CH2+) by short, intense laser pulses were simulated by Born-Oppenheimer molecular dynamics (BOMD) on the ground state potential energy surface using the B3LYP/6-31 + G(d,p) level of theory and a 10 cycle 7 µm cosine squared pulse with a maximum field strength of 0.07 au. Laser fields polarised along the C=C=C axis deposits an average of 150 kcal/mol in the molecule, compared to only 25 and 51 kcal/mol for perpendicular polarisations. Approximately 90% of the trajectories with the field aligned with the C=C=C axis underwent one or more structural rearrangement steps to form H2C=CH–CH+ (15%), H3CCCH+ (4%), cyclopropene cation (6%), and allene cation with rearranged hydrogens and carbons (47%). In addition, a variety of fragments including H2CCCH+ + H (10%), c-C3H3+ + H (7%), and HCCCH+ + H2 (2%) trajectories were produced after isomerisation. With the same amount of thermal energy, field-free BOMD shows good agreements with the BOMD with the field. However, RRKM calculations favour isomerisation to propyne cation and dissociation to HCCCH+ + H2. This suggests that for molecules in intense laser fields the energy in the intermediate isomers is not distributed statistically.

Resonance-like enhancement in high-order above threshold ionization of atoms and molecules in intense laser fields.

We investigate the high-order above-threshold ionization (HATI) of atoms (Ar and Xe) and molecules (N2 and O2) subjected to strong laser fields by numerically solving time-dependent Schrödinger equation. It is demonstrated that resonance-like enhancement of groups of adjacent peaks in photoelectron spectrum of HATI is observed for Ar, Xe, and N2, while this peculiar phenomenon is absent for O2, which is in agreement with experimental observation [ Phys. Rev. A88, 021401 (2013)]. In addition, analysis indicates that resonance-like enhancement in HATI spectra of atoms and molecules is closely related to excitation of the high-lying excited states.

Comparison study for multiple ionization of carbonyl sulfide by linearly and circularly polarized intense femtosecond laser fields using Coulomb explosion imaging

We studied the relative yields and dissociation dynamics for two- and three-body Coulomb explosion (CE) channels from highly charged carbonyl sulfide molecules in intense laser fields using the CE imaging technique. The electron recollision contributions are evaluated by comparing the relative yields for the multiple ionization process in linearly polarized and circularly polarized (LP and CP) laser fields. The nonsequential multiple ionization is only confirmed for the charge states of 2 to 4 because the energy for further ionization from the inner orbital is much larger than the maximum recollision energy, 3.2Up. The novel deviations of kinetic energy releases distributions between LP and CP pulses are observed for the charge states higher than 4. It can be attributed to the stronger molecular bending in highly charged states before three-body CE with CP light, in which the bending wave packet is initialed by the triple or quartic ionization and spread along their potential curves. Compared to LP light, CP light ionizes a larger fraction of bending molecules in the polarization plane.

Vibrational and electronic excitation of ionized nitrogen molecules in intense laser fields

Vibrational and electronic excitation of ionized nitrogen molecules in intense laser fields

The importance of Rydberg orbitals in dissociative ionization of small hydrocarbon molecules in intense laser fields

Much of our intuition about strong-field processes is built upon studies of diatomic molecules, which typically have electronic states that are relatively well separated in energy. In polyatomic molecules, however, the electronic states are closer together, leading to more complex interactions. A combined experimental and theoretical investigation of strong-field ionization followed by hydrogen elimination in the hydrocarbon series C2D2, C2D4 and C2D6 reveals that the photofragment angular distributions can only be understood when the field-dressed orbitals rather than the field-free orbitals are considered. Our measured angular distributions and intensity dependence show that these field-dressed orbitals can have strong Rydberg character for certain orientations of the molecule relative to the laser polarization and that they may contribute significantly to the hydrogen elimination dissociative ionization yield. These findings suggest that Rydberg contributions to field-dressed orbitals should be routinely considered when studying polyatomic molecules in intense laser fields.

Ultrafast proton migration and Coulomb explosion of methyl chloride in intense laser fields

We investigated the ultrafast proton migration and the Coulomb explosion (CE) dynamics of methyl chloride (CH3Cl) in intense femtosecond laser fields at the wavelengths of 800 nm (5.5 × 1014 W/cm2) and 400 nm (4 × 1014 W/cm2), respectively. Various fragment channels from molecular dication and trication were observed by coincidence momentum imaging through the measurement of their kinetic energy releases (KERs). The proton migration from different charged parent ions was analyzed from the obtained KER distributions. For the direct CE channel of CH3+ + Cl+ and CH3+ + Cl2+, the contribution of multiply excited electronic states and multicharged states is identified. In addition, the measurements of relative yields of the fragmentation channel at different laser wavelengths provide a selective control of proton migration for CH3Cl molecules in intense laser fields.