Charge Resonance Enhanced Ionization Research Articles

Generation of the high-intensity single harmonic energy peak and attosecond pulse by using resonance ionization schemes from atoms and molecules

The lower harmonic intensity is still the reason that limits the application of attosecond pulse. Thus, in this paper, on the basis of resonance ionization schemes, we propose the effective methods to improve the harmonic intensity of atomic and molecular systems. For atomic system (i.e. He atom), with the combination of chirped-UV pulse, not only the harmonic cutoff can be extended, but also the harmonic intensity can be enhanced, caused by the UV resonance ionization between ground state and excited state. As a result, the single harmonic energy peak (HEP) with the higher intensity and higher emitted photon energy can be obtained, which can support the attosecond pulses shorter than 40 as. For the molecular system (i.e. [Formula: see text] and [Formula: see text]), by properly choosing the pulse duration of the fundamental pulse, the time region of charge resonance enhanced ionization (CREI) can be well controlled. Therefore, the maximum HEP with the higher intensity can be obtained. Second, by properly adding a half-cycle unipolar pulse, the selected maximum HEP in the CREI region can be further extended. Thus, an intense and broad spectral region can be produced, which can generate the attosecond pulses with durations of 36[Formula: see text]as.

Electron‐Nuclear Dynamics in Molecular Harmonic Generation Driven by a Plasmonic Nonhomogeneous Field

Electron (z)‐nuclear (R) dynamics in the molecular high‐order harmonic generation (MHHG) from H2+ driven by the plasmonic nonhomogeneous field, generated by the surface plasmon polaritons in the bowtie‐shaped nanostructure, have been theoretically investigated through solving the two dimensional time‐dependent Schrödinger equation with the Non‐Bohn‐Oppenheimer approximation. It is found that (i) due to the plasmonic enhancement of the laser intensity, the harmonic cutoff can be extended when the spatial position of H2+ is away from the gap center of the nanostructure. However, due to the limit of the gap size, the threshold value of the harmonic cutoff can be obtained at a given position of H2+. (ii) Due to the asymmetric enhancement of the laser intensity in space, the extended higher harmonics are respectively from E(t) > 0 a.u. or E(t) < 0 a.u. for the cases of the positive and the negative spatial position of H2+. As a result, the intensities of the extended higher harmonics are different and can be controlled by changing the carrier‐envelope phase and the pulse duration of the laser field. (iii) In the few‐cycle pulse duration, the MHHG mainly comes from the multi‐photon resonance ionization (MPRI), while as the pulse duration increases, the MPRI, the charge‐resonance enhanced ionization (CREI) and even the dissociative ionization (DI) are contributed to the MHHG. Moreover, as the spatial position of H2+ moves, the contributions of the MHHG from the MPRI, the CERI and the DI can be controlled. (iv) The contributions of the MHHG from the two‐H nuclei have been investigated and found that when E(t) > 0 a.u., the intensities of the harmonics from the negative‐H is higher than those from the positive‐H; while when E(t) < 0 a.u., the intensities of the harmonics from the positive‐H plays the main role in the MHHG. Moreover, the multi‐minima, caused by the two‐center interference can also be found. (v) Finally, by superposing a properly selected harmonics, a single isolated attosecond pulse (SIAP) with the full width at half maximum (FWHM) of 34 as can be obtained.

Chirp control of multi-photon resonance ionization and charge-resonance enhanced ionization on molecular harmonic generation

The effects of the multi-photon resonance ionization (MPRI) and the charge-resonance enhanced ionization (CREI) on the molecular high-order harmonic generation (MHHG) from H2+ have been investigated by using the chirped pulses. It is found that the MHHG only comes from the MPRI in the shorter pulse duration. As the pulse duration increases, both the MPRI and the CREI contribute to the MHHG. But the MPRI plays the main role in the generations of the above-threshold harmonics and the CREI mainly contributes to the below-threshold harmonics. With the introductions of the up-chirped and the down-chirped pulses, the contributions of the MHHG from the CREI and the MPRI can be enhanced, respectively. Finally, the isotopic investigation (e.g. T2+) shows that due to the slower nuclear motion of the heavy nuclei, the contributions of MHHG from the CERI can be suppressed in the heavy nuclei.

R-dependent molecular harmonic generation from [formula omitted

R-dependent high-order harmonic spectra (R is the nuclear distance) from H2+ have been investigated through solving the Non-Bohn–Oppenheimer time-dependent Schrödinger equation. We found that (i) for the case of the few-cycle pulse, the harmonic emission mainly occurs from R=3.7 to R=6, caused by the charge-resonance-enhanced-ionization (CREI) process. (ii) For the case of the multi-cycle pulse, the harmonic emission can be separated into two parts, that is the charge-resonance-enhanced-ionization region from R=3.7 to R=8; and the dissociative ionization region when R>10. (iii) Isotopic investigation showed that the R-dependent harmonic emission process can be moved towards the smaller-R region as the masses of the nuclei are increased (D2+ and T2+). (iv) Multi-minima on the harmonic spectra can be obtained, which is attributed to the two-center interference and the electron–nuclear coupling during the generation of the harmonics. The R-dependent ionization probabilities, the time-dependent nuclear motions and the time–frequency analyses of the harmonic spectra have been shown to explain the R-dependent molecular harmonic emission process.

Laser-induced dissociative ionization of H2 from the near-infrared to the mid-infrared regime

We apply the Monte Carlo Wave Packet (MCWP) approach to investigate the kinetic energy release (KER) spectra of the protons following double ionization in H$_{2}$ when interacting with laser pulses with central wavelengths ranging from the near-IR (800 nm) to the mid-IR (6400 nm) regions and with durations of 3-21 laser cycles. We uncover the physical origins of the peaks in the nuclear KER spectra and ascribe them to mechanisms such as ionization following a resonant dipole transition, charge-resonance-enhanced ionization (CREI) and ionization in the dissociative limit of large internuclear distances. For relatively large pulse durations, i.e., for 15 or more laser cycles at 3200 nm and 10 or more at 6400 nm, it is possible for the nuclear wave packet in H$_{2}^{+}$ to reach very large separations. Ionization of this part of the wave packet results in peaks in the KER spectra with very low energies. These peaks give direct information about the dissociative energy in the $2p\sigma_{u}$ potential energy curve of H$_{2}^{+}$ at the one- and three-photon resonances between the $2p\sigma_{u}$ and $1s\sigma_{g}$ curves in H$_{2}^{+}$. With the MCWP approach, we perform a trajectory analysis of the contributions to the KER peaks and identify the dominant ionization pathways. Finally, we consider a pump-probe scheme by applying two delayed pulses to track the nuclear dynamics in a time-resolved setting. Low-energy peaks appear for large delays and these are used to obtain the $2p\sigma_{u}$ dissociative energy values at the one-photon resonance between the $2p\sigma_{u}$ and $1s\sigma_{g}$ curves in H$_{2}^{+}$ for different wavelengths.

Electronic dynamics of charge resonance enhanced ionization probed by laser-induced alignment in C2H2

Although charge resonance enhanced ionization (CREI) be an ubiquitous effect in molecules in strong laser fields, the associated electron emission remains difficult to deal with. The main reason relies on the fact that CREI is part of an overall multielectron ionization, where the initial steps of single and dissociative ionization of neutral species dominate the electron spectrum. Using the rescattered electrons, we show that it is possible to address the electron signal from CREI without any contribution from other electron signals. The electrons from CREI are preferentially emitted when the molecular axis is parallel to the laser electric field as expected from its electronic dynamics. Acetylene is chosen for demonstration purpose because single ionization, which is not related to CREI, is more pronounced when the C2H2 molecular axis is perpendicular to the laser electric field.

Internuclear-distance-dependent ionization of H2+ in strong laser field in a classical perspective

Ionizations of atoms and molecules in strong laser fields are fundamental processes of ultrafast physics. Compared with atom ionization, molecular ionization is very complex due to the existence of multi Coulomb centers. As a simplest molecule, H2+ has been widely used to explore new phenomena of molecules in strong laser fields. One of the notable processes in H2+ ionization is charge resonance enhanced ionization (CREI), in which the ionization rate is enhanced substantially when the internuclear distances are around 6 a.u. and 10 a.u. CREI has been extensively studied by numerically simulating the time-dependent Schrödinger equation. While quantum calculations provide accurate ionization rates, the mechanism governing the CREI is not revealed in such ab-initio calculations. On the contrary, the calculations based on the classical trajectories Monte-Carlo assembly may offer an intuitive picture for CREI though some quantum information is not included. In this paper, we revisit the CREI of H2+ in a strong infrared laser field by Monte-Carlo simulation. By initializing ten-thousand classical points whose initial positions and velocities satisfy the field-free Hamiltonian of H2+, we solve the classical Newtonian equation and obtain the trajectories of all particles, from which one may analyze the particle velocities, energies, etc. We count the ionization events by diagnosing the particle energy after the laser interaction. If the sum of the kinetic energy and potential energy is larger than 0, we set it as an ionization event. The ionization rate is calculated by collecting all ionization events and normalizing it with the total particle number involved in the calculation. By setting the internuclear distances to be different values, we obtain the ionization rate as a function of internuclear distance. Our simulation shows that the ionization probability is greatly enhanced when the internuclear distance is about 5 to 6 a.u. by employing a 1064 nm, 4×1013 W/cm2, five cycles laser pulse. By tracing the particle trajectory, we find that the electron usually gains the energy from the laser field by circulating one nucleus, then passes through the interatomic barrier and moves around the other nucleus before being ionized. By looking into the relationship between the ionization probability and the laser-distorted Coulomb potential at different internuclear distances, we find that the ionization probability is maximum when the energy difference between the ground state and the interatomic Coulomb barrier, or between the ground state and the saddle value of the laser-distorted potential, is minimum. The classical calculation of the ionization of H2+ interacting with intense laser field reproduces the qualitative features of the corresponding quantum-mechanical calculation. It offers an intuitive physical picture of the tunneling ionization of molecules through investigating the classical trajectories and provides a new perspective to inspect the intriguing phenomena in quantum systems.

Intensity-dependent study of strong-field Coulomb explosion of H2.

We demonstrate experimentally that in pump-probe experiment of H2 fragmentation by intense laser fields, the Coulomb explosion (CE) paths induced by the second ionization of dissociating H2+ show varied dependencies on the laser intensity. While the charge resonance enhanced ionization (CREI) channel is intensity dependent, the probe induced CE (PICE) channel is intensity independent at certain delay time. By using a classical model, we calculated the dissociation trajectories which agree well with the experimental data.

Alignment-dependent ionization of H2+: From multiphoton ionization to tunneling ionization

We investigate the strong-field ionization for the ground state of H${{}_{2}}^{+}$ by numerically solving the three-dimensional (3D) time-dependent Schr\odinger equation (TDSE), and comparisons have been made among the TDSE, the different versions of molecular strong-field approximation (MO-SFA) and the molecular Ammosov-Delone-Krainov (MO-ADK) approximation. The study shows that, for the TDSE results, the ratio of ionization rates between perpendicular and parallel alignments displays a step-like structure against the Keldysh parameter $\ensuremath{\gamma}$. For small internuclear distances, the transition between the steps are found to be around $\ensuremath{\gamma}\ensuremath{\approx}1$ and is recognized as the competition between the multiphoton ionization (MPI) and tunneling ionization (TI). The ionization is more isotropic in the MPI regime. For large internuclear distances, the transition position shifts to larger $\ensuremath{\gamma}$ due to the charge-resonance-enhanced ionization (CREI). Different versions of strong-field ionization theories are compared against the TDSE results.

Charge Resonance Enhanced Ionization ofCO2Probed by Laser Coulomb Explosion Imaging

The process by which a molecule in an intense laser field ionizes more efficiently as its bond length increases towards a critical distance R(c) is known as charge resonance enhanced ionization (CREI). We make a series of measurements of this process for CO(2), by varying pulse duration from 7 to 200 fs, in order to identify the charge states and time scales involved. We find that for the 4+ and higher charge states, 100 fs is the time scale required to reach the critical geometry <R(CO)> ≈ 2.1 Å and <θ(OCO)> ≈ 163° (equilibrium CO(2) geometry is <R(CO)> ≈ 1.16 Å and <θ(OCO)> ≈ 172°). The CO(2)(3+) molecule, however, appears always to begin dissociation from closer than 1.7 Å indicating that dynamics on charge states lower than 3+ is not sufficient to initiate CREI. Finally, we make quantum ab initio calculations of ionization rates for CO(2) and identify the electronic states responsible for CREI.

Effects of laser pulse duration and intensity on Coulomb explosion of CO2: Signatures of charge-resonance enhanced ionization

We studied laser-induced Coulomb explosion of CO2 by full triple-coincidence momentum resolved detection of resulting ion fragments. From the coincidence momentum data we can reconstruct molecular geometry immediately before explosion. We observe the dynamics of Coulomb explosion by comparing reconstructed CO2 geometries for different Ti:Sapphire laser pulse durations (at the same intensity) ranging from few cycles (7 fs) to 200 fs. We conclude that for longer pulse durations (≥100 fs) Coulomb explosion proceeds through the enhanced ionization mechanism taking place at the critical O-O distance of 8 a.u., similarly to well known charge-resonance enhanced ionization (CREI) in H2.

Double-Exponentially Decayed Photoionization in CREI Effect: Numerical Experiment on 3D H2+

On the platform of the 3D H2+ system, we perform a numerical simulation of its photoionization rate under excitation of weak to intense laser intensities with varying pulse durations and wavelengths. A novel method is proposed for calculating the photoionization rate: a double exponential decay of ionization probability is best suited for fitting this rate. Confirmation of the well-documented charge-resonance-enhanced ionization (CREI) effect at medium laser intensity and finding of ionization saturation at high light intensity corroborate the robustness of the suggested double-exponential decay process. Surveying the spatial and temporal variations of electron wavefunctions uncovers a mechanism for the double-exponentially decayed photoionization probability as onset of electron ionization along extra degree of freedom. Henceforth, the new method makes clear the origins of peak features in photoionization rate versus internuclear separation. It is believed that this multi-exponentially decayed ionization mechanism is applicable to systems with more degrees of motion.

An alternative way for computing absolute and normalized photoionization rates: Tested in 1D H2+ system

In this article, we deployed a semi-classical non-Born–Oppenheimer 1D H 2 + model for investigating interactions of intense laser with H 2 + ionic system by treating the protons as classical particles and the electron as a quantum one. A novel analytical algorithm was developed for calculating absolute and normalized ionization rates in this fully dynamic model. By analyzing thus-derived instantaneous ionization rates as a function of internuclear separation, we observed numerically an obvious CREI (charge resonance enhanced ionization) effect in certain laser intensity range in relation with core-softening parameters, as well as its absence or reduction under higher laser intensities, which corroborated the robustness of our proposed algorithm. Electron’s probability oscillation, proving the causal relation between ionization enhancement and charge resonance process, between the two potential wells was also observed and analyzed.

Molecular above-threshold-ionization spectra: The effect of moving nuclei

Exact non-Born-Oppenheimer simulations of a one-dimensional model of one-electron ${\mathrm{H}}_{2}^{+}$ and linear ${\mathrm{H}}_{3}^{2+}$ in an intense short laser pulse are used to investigate the nonlinear multiphoton electron emission spectra, called above threshold ionization (ATI). Due to the rapid proton motion on near-femtosecond time scale, the ATI spectra are found to be produced at the critical internuclear distance ${R}_{c}\ensuremath{\sim}7--8\mathrm{a}.\mathrm{u}.,$ leading to charge-resonance-enhanced ionization (CREI). As a consequence, maxima in the ATI spectra are displaced with respect to the similar H-atom spectra by a laser-induced Stark energy ${E}_{M}{R}_{c}/2,$ where ${E}_{M}$ is the maximum amplitude of the laser field. Highly oscillating ATI spectra occur, which are enhanced by the nuclear motion. These are interpreted as due to coherent excitations of the lowest unoccupied molecular orbitals and highest occupied molecular orbitals, which are also responsible for CREI. Electron rescattering effects in the energy regions of ${10U}_{p}$ and ${8U}_{p},$ where ${U}_{p}$ is the ponderomotive energy, are shown to be substantially reduced due to the rapid molecular dissociation and Coulomb explosion. Nevertheless, the ATI spectra in these energy regions reflect the different electron energies in the rescattering process. Fine structures of the ATI spectra are found to be enhanced by moving nuclei, reflecting the enhancement of resonant transitions by varying Franck-Condon factors during the nuclear motion.

Enhanced ionization of the molecular ionH2+in intense laser and static magnetic fields

The three-dimensional time-dependent Schr\"odinger equation is solved exactly for the ${\mathrm{H}}_{2}^{+}$ molecular ion as a function of internuclear distance R in a short intense laser field pulse and a static magnetic field, parallel to the internuclear axis, using a numerical integration method. Previous calculations of laser-induced ionization in this ion for zero magnetic field [Phys. Rev. A 48, 3837 (1993); 52, 2511 (1995)] demonstrated the phenomenon of charge-resonance-enhanced ionization (CREI) at critical distances ${R}_{c},$ due to Stark displacements of the lowest unoccupied molecular orbital (LUMO) above internal proton Coulomb and static laser field barriers. The presence of the magnetic field allows for controlling the energy displacements of the LUMO and consequently control of CREI, thus confirming CREI as a quasistatic electron tunneling process in the nonsymmetric double-well potential created by protons and a laser field.

Laser control of molecular ionization with intense short laser pulses

Numerical solutions of the time-dependent Schroedinger equation of the two molecules H 2 + and H 2 allow for nonperturbative calculations of ionization rates in short intense laser pulses (τ < 1 ps, I ≃ 10 14 W/cm 2). It is shown that the coherent superposition of two pulses of frequency ω and 2ω results in optimal control of the ionization process at critical internuclear distances R c where charge resonance enhanced ionization (CREI) occurs. The implications of CREI are discussed for laser control of ionization in mass spectrometry.

Charge-resonance-enhanced ionization of molecular ions in intense laser pulses: Geometric and orientation effects

Numerical solutions of the time-dependent Schr\odinger equation for one-electron two-dimensional ${\mathrm{H}}_{2}^{+},$ ${\mathrm{H}}_{3}^{2+}$ molecular ions have been obtained in order to illustrate the dependence of charge-resonance-enhanced ionization (CREI) on the angular orientation of the molecule. For ${\mathrm{H}}_{3}^{2+}$ both linear and triangular geometries have been considered. It is found, in general, that orientational effects on ionization rates, laser-induced dipole moments and torques, are most significant at the critical distances ${R}_{c}$ and critical angles ${\ensuremath{\varphi}}_{c}$ of molecular geometry where CREI occurs. The calculated ionization rates and field-induced torques are used to estimate alignment times near the dissociative ionization regime of these ions in intense laser pulses. It is found that orientational trapping can occur in this regime at the critical CREI configurations.

Exact numerical calculations of dissociative-ionization of molecular ions in intense laser fields: Non-Born-Oppenheimer dynamics

The time-dependent Schrödinger equation for the 1-D H2+ molecule (with both nuclear and electronic degrees of freedom included) was solved numerically. A wave–function splitting technique was used, which allows one to circumvent the problem of lost information due to commonly used absorbing boundaries of the electron flux. This technique allows us to calculate the above-threshold ionization (ATI) photoelectron kinetic energy spectra in the presence of moving nuclei, as well as complete spectra of dissociating protons, beyond the Born–Oppenheimer approximation. A considerable enhancement of the ATI spectra, with respect to the spectra generated by a H atom, were found. The peaks seen in calculated Coulomb explosion spectra of protons agree well with the predictions of recent theoretical work related to the phenomenon of charge-resonance-enhanced ionization (CREI). © 1997 John Wiley & Sons, Inc. Int J Quant Chem 65: 503–512, 1997

Phase control of molecular ionization: H2 + and H3 2+ in intense two-color laser fields.

Charge resonance-enhanced ionization is examined for combinations of intense, linearly polarized laser fields, and their second harmonic (1\ensuremath{\omega}-2\ensuremath{\omega}) for both a diatomic molecular ion (${\mathrm{H}}_{2}$${\mathrm{}}^{+}$) and an asymmetric linear triatomic molecular ion (${\mathrm{H}}_{3}$${\mathrm{}}^{2+}$). Ionization is found to be strongly dependent on the relative phase between the two colors in both cases. In particular for ${\mathrm{H}}_{2}$${\mathrm{}}^{+}$ one can achieve nearly complete ionization of electrons at one of the nuclei only. For the asymmetric linear triatomic molecular ion (${\mathrm{H}}_{3}$${\mathrm{}}^{2+}$) enhanced ionization is shown also to occur at large critical distances. In the presence of two color fields, the ionization rate of the asymmetric ${\mathrm{H}}_{3}$${\mathrm{}}^{2+}$ can be controlled again by tuning the relative phase between the driving fields. The phase control of the enhanced ionization can be rationalized in terms of field-induced over-the-barrier ionization and laser-induced electron localization or equivalently electron tunneling suppression. \textcopyright{} 1996 The American Physical Society.

Dissociative ionization ofH2+in an intense laser field: Charge-resonance-enhanced ionization, Coulomb explosion, and harmonic generation at 600 nm

The time-dependent Schr\"odinger equation for ${\mathrm{H}}_{2}$${\mathrm{}}^{+}$ in a 600-nm, intense (I\ensuremath{\geqslant}${10}^{14}$ W/${\mathrm{cm}}^{2}$) laser field is solved numerically for a model which uses the exact three-body Hamiltonian with one-dimensional nuclear motion restricted to the direction of the laser electric field and three-dimensional electronic motion. High ionization rates of ${\mathrm{H}}_{2}$${\mathrm{}}^{+}$ are found, exceeding those of neutral atomic hydrogen. This confirms, by the rigorous, full dynamical calculation, the recently discovered charge-resonance-enhanced ionization (CREI)---all previous demonstrations of CREI were based on the ``frozen nuclei'' model. The numerical kinetic-energy spectra of dissociating fragments are compared with recent experimental results. They can be interpreted by a simple bond softening mechanism (or laser-induced avoided crossing in a dressed-state representation), in which the binding forces are completely suppressed by the strong electric field and thus the dissociating fragments move as free particles with a kinetic energy close to their initial vibrational energy until they reach a critical distance R=${\mathit{R}}_{\mathit{c}}$\ensuremath{\cong}8 bohr, where they are rapidly ionized, due to CREI. The harmonic generation spectra calculated from our non-Born-Oppenheimer simulations show that the high harmonics are also generated when the nuclei cross this critical distance R=${\mathit{R}}_{\mathit{c}}$. \textcopyright{} 1996 The American Physical Society.