Control of electron excitation and localization in the dissociation of H2(+) and its isotopes using two sequential ultrashort laser pulses

Proton tunneling in the dissociation of H2+ and its asymmetric isotopologues driven by circularly polarized THz laser pulses

Light-induced deprotonation of molecules is an important process in photochemical reactions. Here, we theoretically investigate the tunneling deprotonation of H2+ and its asymmetric isotopologues driven by circularly polarized THz laser pulses. The quasi-static picture shows that the field-dressed potential barrier is significantly lowered for the deprotonation channel when the mass asymmetry of the diatomic molecule increases. Our numerical simulations demonstrate that when the mass symmetry breaks, the tunneling deprotonation is significantly enhanced and the proton tunneling becomes the dominant dissociation channel in the THz driving fields. In addition, the simulated nuclear momentum distributions show that the emission of the proton is directed by the effective vector potential for the deprotonation channel and, meanwhile, the angular distribution of the emitting proton is affected by the alignment and rotation of the molecule induced by the rotating field.

Multiphoton Ionization Reduction of Atoms in Two-Color Femtosecond Laser Fields

We report the ionization reduction of atoms in two-color femtosecond laser fields in this joint theoretical-experimental study. For the multiphoton ionization of atoms using a 400 nm laser pulse, the ionization probability is reduced if another relatively weak 800 nm laser pulse is overlapped. Such ionization reduction consistently occurs regardless of the relative phase between the two pulses. The time-dependent Schrödinger equation simulation results indicate that with the assisted 800 nm photons the electron can be launched to Rydberg states with large angular quantum numbers, which stand off the nuclei and thus are hard to be freed in the multiphoton regime. This mechanism works for hydrogen, helium, and probably some other atoms if two-color laser fields are properly tuned.

Electron transfer in strong-field three-body fragmentation of ArKr2 trimers

We experimentally studied the three-body fragmentation dynamics of a noble gas cluster (ArKr₂) upon its multiple ionization by an intense femtosecond laser pulse. The three-dimensional momentum vectors of correlated fragmental ions were measured in coincidence for each fragmentation event. A novel comet-like structure was observed in the Newton diagram of the quadruple-ionization-induced breakup channel of ArKr₂ ⁴⁺→ Ar⁺ + Kr⁺ + Kr²⁺. The concentrated head part of the structure mainly originates from the direct Coulomb explosion process, while the broader tail part of the structure stems from a three-body fragmentation process involving electron transfer between the distant Kr⁺ and Kr²⁺ ion fragments. Due to the field-driven electron transfer, the Coulomb repulsive force of the Kr²⁺ and Kr⁺ ions with respect to the Ar⁺ ion undergoes exchange, leading to changes in the ion emission geometry in the Newton plot. An energy sharing among the separating Kr²⁺ and Kr⁺ entities was observed. Our study indicates a promising approach for investigating the strong-field-driven intersystem electron transfer dynamics by using the Coulomb explosion imaging of an isosceles triangle van der Waals cluster system.

Exact Factorization Adventures: A Promising Approach for Non-Bound States

Modeling the dynamics of non-bound states in molecules requires an accurate description of how electronic motion affects nuclear motion and vice-versa. The exact factorization (XF) approach offers a unique perspective, in that it provides potentials that act on the nuclear subsystem or electronic subsystem, which contain the effects of the coupling to the other subsystem in an exact way. We briefly review the various applications of the XF idea in different realms, and how features of these potentials aid in the interpretation of two different laser-driven dissociation mechanisms. We present a detailed study of the different ways the coupling terms in recently-developed XF-based mixed quantum-classical approximations are evaluated, where either truly coupled trajectories, or auxiliary trajectories that mimic the coupling are used, and discuss their effect in both a surface-hopping framework as well as the rigorously-derived coupled-trajectory mixed quantum-classical approach.

Seemingly asymmetric atom-localized electronic densities following laser-dissociation of homonuclear diatomics

Recent experiments on laser-dissociation of aligned homonuclear diatomic molecules show an asymmetric forward-backward (spatial) electron-localization along the laser polarization axis. Most theoretical models attribute this asymmetry to interference effects between gerade and ungerade vibronic states. Presumably due to alignment, these models neglect molecular rotations and hence infer an asymmetric (post-dissociation) charge distribution over the two identical nuclei. In this paper, we question the equivalence that is made between spatial electron-localization, observed in experiments, and atomic electron-localization, alluded by these theoretical models. We show that (seeming) agreement between these models and experiments is due to an unfortunate omission of nuclear permutation symmetry, i.e., quantum statistics. Enforcement of the latter requires mandatory inclusion of the molecular rotational degree of freedom, even for perfectly aligned molecules. Unlike previous interpretations, we ascribe spatial electron-localization to the laser creation of a rovibronic wavepacket that involves field-free molecular eigenstates with opposite space-inversion symmetry i.e., even and odd parity. Space-inversion symmetry breaking would then lead to an asymmetric distribution of the (space-fixed) electronic density over the forward and backward hemisphere. However, owing to the simultaneous coexistence of two indistinguishable molecular orientational isomers, our analytical and computational results show that the post-dissociation electronic density along a specified space-fixed axis is equally shared between the two identical nuclei-a result that is in perfect accordance with the principle of the indistinguishability of identical particles.

Proposal for Measuring Electron Displacement Induced by a Short Laser Pulse

In laser-matter interaction, most previous studies have focused on the change of the electron momentum induced by the external fields. Here, we theoretically investigate the electron displacement induced by an ultrashort pulse, whose precise waveform is hard to determine experimentally. We propose and numerically demonstrate a scheme to accurately measure the electron displacement using a ruler formed by the interfering spirals in the photoelectron momentum distribution generated by two oppositely circularly polarized pulses. The scheme is robust against the focusing volume effects and the jitter of the carrier envelope phase of the two circular pulses. The ability to measure the electron displacement by an arbitrary pulse may pave the way to quantitative control of the charge migration in matter on the scale of Ångström.

Angle-dependent electron-electron correlation in the single ionization of H2 in strong laser fields

The one-photon ionization and tunneling ionization of H₂ exposed to strong XUV and infrared laser pulses are studied by numerically simulating the four-dimensional time-dependent Schrödinger equation, which includes two-electron dynamics for arbitrary angle between the molecular axis and the laser polarization direction. In the one-photon single ionization of H₂, one electron escapes fast and the other bound electron is not disturbed but remains in coherent superposition of two electronic states of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\bf{H}}}_{{\bf{2}}}^{{\boldsymbol{+}}}$$\end{document}H2+. In another case, under the irradiation of strong infrared laser pulses, one electron tunnels through the laser-dressed Coulomb barrier, and the other bound electron has enough time to adapt to the potential of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\bf{H}}}_{{\bf{2}}}^{{\boldsymbol{+}}}$$\end{document}H2+ and thus is prone to transfer to the ground electronic state of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\bf{H}}}_{{\bf{2}}}^{{\boldsymbol{+}}}$$\end{document}H2+. In the intermediate regime, between the one photon and tunneling regimes, this electron-electron correlation depends strongly on the laser frequency, laser intensity and on the angle between laser polarization and the molecular axis.

A redshift mechanism of high-order harmonics: Change of ionization energy

We theoretically study the high-order harmonic generation of H₂⁺ and its isotopes beyond the Born-Oppenheimer dynamics. It is surprising that the spectral redshift can still be observed in high harmonic spectra of H₂⁺ driven by a sinusoidal laser pulse in which the trailing (leading) edge of the laser pulse is nonexistent. The results confirm that this spectral redshift originates from the reduction in ionization energy between recombination time and ionization time, which is obviously different from the nonadiabatic spectral redshift induced by the falling edge of the laser pulse. Additionally, the improved instantaneous frequency of harmonics by considering the changeable ionization energy can deeply verify our results. Therefore, this new mechanism must be taken into account when one uses the nonadiabatic spectral redshift to retrieve the nuclear motion.

Monitoring the electron dynamics of the excited state via higher-order spectral minimum

A pump-probe scheme for monitoring the electron dynamics of the excited state has been investigated by numerically solving the two-state time-dependent Schrödinger equation based on the non-Born-Oppenheimer approximation. By adjusting the delay time between a mid-infrared probe pulse and an ultra violet pump pulse, an obvious minimum can be seen in the higher-order harmonic region. With electron probability density distribution, ionization rate and classical simulation, the minimum can be ascribed to the electron localization around one nucleus at larger delay time and represents the electron dynamics of the excited state at the time of ionization. Moreover, the position of the minimum is much more sensitive to the nuclear motion.

Observing electron localization in a dissociating H2+ molecule in real time

Dissociation of diatomic molecules with odd number of electrons always causes the unpaired electron to localize on one of the two resulting atomic fragments. In the simplest diatomic molecule H₂⁺ dissociation yields a hydrogen atom and a proton with the sole electron ending up on one of the two nuclei. That is equivalent to breaking of a chemical bond-the most fundamental chemical process. Here we observe such electron localization in real time by performing a pump-probe experiment. We demonstrate that in H₂⁺ electron localization is complete in just 15 fs when the molecule's internuclear distance reaches 8 atomic units. The measurement is supported by a theoretical simulation based on numerical solution of the time-dependent Schrödinger equation. This observation advances our understanding of detailed dynamics of molecular dissociation.

Strong Field Theories beyond Dipole Approximations in Nonrelativistic Regimes

The exact nondipole Volkov solutions to the Schrödinger equation and Pauli equation are found, based on which a strong field theory beyond the dipole approximation is built for describing the nondipole effects in nonrelativistic laser driven electron dynamics. This theory is applied to investigate momentum partition laws for multiphoton and tunneling ionization and explicitly shows that the complex interplay of a laser field and Coulomb action may reverse the expected photoelectron momentum along the laser propagation direction. The magnetic-spin coupling does not bring observable effects on the photoelectron momentum distribution and can be neglected. Compared to the strong field approximation within the dipole approximation, this theory works in a much wider range of laser parameters and lays a solid foundation for describing nonrelativistic electron dynamics in both short wavelength and midinfrared regimes where nondipole effects are unavoidable.

Dissociation and Ionization of Quasi-Periodically Vibrating H2+ in Intense Few-Cycle Mid-Infrared Laser Fields

Using quantum mechanics calculations, we theoretically study the dissociation and ionization dynamics of the hydrogen-molecule ion in strong laser fields. Having prepared the nuclear wave packet of H₂⁺ in a specific vibrational state, a pump laser is used to produce a vibrational excitation, leading to quasi-periodical vibration without ionization. Then, a time-delayed few-cycle laser is applied to trigger the dissociation or ionization of H₂⁺. Both the time delay and the intensity of the probe laser alter the competition between dissociation and ionization. We also explore the dependence of kinetic-energy release spectra of fragments on the time delay, showing that the channels of above-threshold dissociation and below-threshold dissociation are opened and closed periodically. Also, dissociation from different channels is influenced by nuclear motion. The dissociation mechanism has been described in detail using the Floquet picture. This work provides a useful method for steering the electronic and nuclear dynamics of diatomic molecules in intense laser fields.

Carrier-Envelope-Phase Characterization for an Isolated Attosecond Pulse by Angular Streaking

The carrier envelope phase (CEP) is a crucial parameter for a few-cycle laser pulse since it substantially determines the laser waveform. Stepping forward from infrared to extreme ultraviolet (EUV) pulses, we propose a strategy to directly characterize the CEP of an isolated attosecond pulse (IAP) by numerically simulating the tunneling ionization of a hydrogen atom in a combined IAP and phase-stabilized circularly polarized IR laser pulse. The fine modulations of the combined laser fields, due to the variation of the CEP of the IAP, are exponentially enlarged onto the distinct time-dependent tunneling ionization rate. Electrons released at different time with distinct tunneling ionization rates are angularly streaked to different directions. By measuring the resulting photoelectron momentum distribution, the CEP of the IAP can be retrieved. The characterization of the CEP of an IAP will open the possibility of capturing sub-EUV-cycle dynamics.

Laser-induced electron localization in H₂⁺: mixed quantum-classical dynamics based on the exact time-dependent potential energy surface

We study the exact nuclear time-dependent potential energy surface (TDPES) for laser-induced electron localization with a view to eventually developing a mixed quantum-classical dynamics method for strong-field processes. The TDPES is defined within the framework of the exact factorization [A. Abedi, N. T. Maitra, and E. K. U. Gross, Phys. Rev. Lett., 2010, 105, 123002] and contains the exact effect of the couplings to the electronic subsystem and to any external fields within a scalar potential. We compare its features with those of the quasistatic potential energy surfaces (QSPES) often used to analyse strong-field processes. We show that the gauge-independent component of the TDPES has a mean-field-like character very close to the density-weighted average of the QSPESs. Oscillations in this component are smoothened out by the gauge-dependent component, and both components are needed to yield the correct force on the nuclei. Once the localization begins to set in, the gradient of the exact TDPES tracks one QSPES and then switches to the other, similar to the description provided by surface-hopping between QSPESs. We show that evolving an ensemble of classical nuclear trajectories on the exact TDPES accurately reproduces the exact dynamics. This study suggests that the mixed quantum-classical dynamics scheme based on evolving multiple classical nuclear trajectories on the exact TDPES will be a novel and useful method to simulate strong field processes.

Coherent electronic wave packet motion in C(60) controlled by the waveform and polarization of few-cycle laser fields

Strong laser fields can be used to trigger an ultrafast molecular response that involves electronic excitation and ionization dynamics. Here, we report on the experimental control of the spatial localization of the electronic excitation in the C_{60} fullerene exerted by an intense few-cycle (4 fs) pulse at 720 nm. The control is achieved by tailoring the carrier-envelope phase and the polarization of the laser pulse. We find that the maxima and minima of the photoemission-asymmetry parameter along the laser-polarization axis are synchronized with the localization of the coherent electronic wave packet at around the time of ionization.

Two-dimensional directional proton emission in dissociative ionization of H(2)

An intense phase-controlled orthogonally polarized two-color ultrashort laser pulse is used to singly ionize and dissociate H_{2} into a neutral hydrogen atom and a proton. Emission-direction and kinetic-energy dependent asymmetric dissociation of H_{2} is observed as a function of the relative phase of the orthogonally polarized two-color pulse. Significant asymmetric proton emission is measured in the direction between two polarization axes. Our numerical simulations of the time-dependent Schrödinger equation reproduce many of the observed features. The asymmetry is attributed to the coherent superposition of two-dimensional nuclear wave packets with opposite parities, which have the same energies and overlap in the same emission directions.

Theoretical investigation of the competitive mechanism between dissociation and ionization of H₂⁺ in intense field

The competitive mechanism between dissociation and ionization of hydrogen molecular ion in intense field has been theoretically investigated by using an accurate non-Born-Oppenheimer method. The relative yield of fragments indicates that the dissociation and ionization channels are competitive with the increasing laser intensity from 5.0 × 10(13) to 2.0 × 10(14) W/cm(2). In the case of intensity lower than 1.0 × 10(14) W/cm(2), the dissociation channel is dominant, with a minor contribution from ionization. The mechanism of dissociation includes the contributions from the bond softening, bond hardening, below-threshold dissociation, and above-threshold dissociation, which are strongly dependent on the laser intensity and initial vibrational state. Furthermore, the ionization dominates over the dissociation channel at the highest intensity of 2.0 × 10(14) W/cm(2). The reasonable origin of ionization is ascribed as the above-threshold Coulomb explosion, which has been demonstrated by the space-time dependent ionization rate. Moreover, the competition mechanism between dissociation and ionization channels are displayed on the total kinetic energy resolved (KER) spectra, which could be tested at current experimental conditions.

Carrier-envelope phase control over pathway interference in strong-field dissociation of H2+

The dissociation of an H2+ molecular-ion beam by linearly polarized, carrier-envelope-phase-tagged 5 fs pulses at 4×10(14) W/cm2 with a central wavelength of 730 nm was studied using a coincidence 3D momentum imaging technique. Carrier-envelope-phase-dependent asymmetries in the emission direction of H+ fragments relative to the laser polarization were observed. These asymmetries are caused by interference of odd and even photon number pathways, where net zero-photon and one-photon interference predominantly contributes at H+ + H kinetic energy releases of 0.2-0.45 eV, and net two-photon and one-photon interference contributes at 1.65-1.9 eV. These measurements of the benchmark H2+ molecule offer the distinct advantage that they can be quantitatively compared with ab initio theory to confirm our understanding of strong-field coherent control via the carrier-envelope phase.

Anomalous isotopic effect on electron-directed reactivity by a 3-μm midinfrared pulse

We have theoretically studied the effect of nuclear mass on electron localization in dissociating H₂⁺ and its isotopes subjected to a few-cycle 3-μm pulse. Our results reveal an anomalous isotopic effect in which the degree of electron-directed reactivity can be even higher for heavier isotopes in the intense midinfrared field. We show, for the first time, the pronounced electron localization can be established through the interferences among the multi-photon coupling channels. Due to the relative enhancement of higher-order coupling channels with growing mass, the interference maxima at different kinetic energy of the spectra gradually become in phase, ultimately resulting in the larger dissociation asymmetries of heavier isotopes.

Enhancing the intense field control of molecular fragmentation

We describe a pump-probe scheme with which the spatial asymmetry of dissociating molecular fragments-as controlled by the carrier-envelope phase of an intense few-cycle laser pulse-can be enhanced by an order of magnitude or more. We illustrate the scheme using extensive, full-dimensional calculations for dissociation of H(2)(+) and include the averaging necessary for comparison with experiment.

THEORETICAL STUDY OF ABOVE THRESHOLD DISSOCIATION OF HD+ IN FEMTOSECOND LASER FIELDS

The above threshold dissociation (ATD) of the HD+ molecular ion in a linearly polarized femtosecond laser field is theoretically studied using three-dimensional time-dependent quantum wave packet method. Based on the Born–Oppenheimer approximation (BOA), calculations are performed on two electronic states, the ground state 1sσ and the excited state 2pσ. The energy-dependent distributions of the dissociated fragments, resulting from the ATD, are calculated by using an asymptotic-flow expression in the momentum space. The numerical results demonstrate that, in the laser field of wavelength λ = 800 nm and full-width at half-maximum (FWHM) τ = 30 fs , only two-photon dissociation is observable at a weaker pulse peak intensity, 5.0 × 1012 W cm -2, while at an intense intensity, 1.5 × 1015 W cm -2, the dissociated fragments resulting from four-photon absorption dominates over the photodissociation process. These results are consistent with the experimental observation of Orr et al. [Orr PA et al., Phys Rev Lett98:163001, 2007]. The ac Stark-shift caused by intense laser field will change the kinetic energies of the fragments. The ATD phenomena are quantitatively interpreted in terms of the concept of light-induced potential. The molecular rotation and alignment have some effects on the kinetic energy spectrum of the dissociated fragments. The molecular rotation reduces the ac Stark-shift and broadens the peaks of kinetic energy spectra of the dissociated fragments. However, the intense laser field can effectively align the molecule and is helpful to increase the ATD probability. The ATD spectrum is related to the initial quantum numbers J0 and M0 of the molecule. The ATD spectrum of HD+ is calculated at a limited thermal temperature.

Phase dependence of electron localization in HeH²⁺ dissociation with an intense few-cycle laser pulse

The electron localization in the dissociation of the asymmetric charged molecular ion HeH²⁺ exposed to an intense few-cycle laser pulse is studied by solving numerically the 3D time-dependent Schrödinger equation. By varying the carrier-envelope phase (CEP) and the intensity of the pulse, the upward shift of the localization probability and the suppression of the dissociation channel He²⁺+H are observed. Our analysis shows that the phenomenon is attributed to the asymmetric structure of the molecule as well as the recollision-assistant field-induced ionization of the electron wave packets localized on H⁺ in the trailing of the pulse.

Control of electron localization in deuterium molecular ions using an attosecond pulse train and a many-cycle infrared pulse

We demonstrate an experimental control of electron localization in deuterium molecular ions created and dissociated by the combined action of an attosecond pulse train and a many-cycle infrared (IR) pulse. The attosecond pulse train is synthesized using both even and odd high order harmonics of the driving IR frequency so that it can strobe the IR field once per IR cycle. An asymmetric ejection of the deuterium ions oscillates with the full IR period when the APT-IR time-delay is scanned. The observed control is due to the creation of a coherent superposition of 1s sigma{g} and 2p sigma{u} states via interference between one-photon and two-photon dissociation channels.

Ion-energy dependence of asymmetric dissociation of D2 by a two-color laser field

Two-color (800 and 400 nm) short (45 fs) linearly polarized pulses are used to ionize and dissociate D2 into a neutral deuterium atom and a deuteron. The yields and energies of the ions are measured left and right along the polarization vector. As the relative phase of the two colors is varied, strong yield asymmetries are found in the ion-energy regions traditionally identified as bond softening, above-threshold dissociation and rescattering. The asymmetries in these regions are quite different. A model based on the dynamic coupling by the laser field of the gerade and ungerade states in the molecular ion accounts for many of the observed features.

Electron localization in molecular fragmentation of H2 by carrier-envelope phase stabilized laser pulses

Fully differential data for H2 dissociation in ultrashort (6 fs, 760 nm), linearly polarized, intense (0.44 PW/cm{2}) laser pulses with a stabilized carrier-envelope phase (CEP) were recorded with a reaction microscope. Depending on the CEP, the molecular orientation, and the kinetic energy release (KER), we find asymmetric proton emission at low KERs (0-3 eV), basically predicted by Roudnev and Esry, and much stronger than reported by Kling et al. Wave packet propagation calculations reproduce the salient features and discard, together with the observed KER-independent electron asymmetry, the first ionization step to be the reason for the asymmetric proton emission.

Strong-field modulated diffraction effects in the correlated electron-nuclear motion in dissociating H(2+)

We show that the electronic dynamics in a molecule driven by a strong field is complex and potentially even counterintuitive. As a prototype example, we simulate the interaction of a dissociating H2+ molecule with an intense infrared laser pulse. Depending on the laser intensity, the direction of the electron's motion between the two nuclei is found to follow or oppose the classical laser-electric force. We explain the sensitive dependence of the correlated electronic-nuclear motion in terms of the diffracting electronic momentum distribution of the dissociating two-center system. The distribution is dynamically modulated by the nuclear motion and periodically shifted in the oscillating infrared electric field.

Attosecond photoelectron spectroscopy of electron tunneling in a dissociating hydrogen molecular ion

We demonstrate the potential of intense-field pump, attosecond probe photoelectron spectroscopy to monitor electron tunneling between the two protons during dissociative ionization of the hydrogen molecule, with attosecond temporal and Angstrom-scale spatial resolution.