Ionization In Strong Laser Fields Research Articles

Multiphoton Resonance Meets Tunneling Ionization: High-Efficient Photoexcitation in Strong-Field-Dressed Ions.

Tunneling ionization, a fascinating quantum phenomenon, has played the key role in the development of attosecond physics. Upon absorption of a few tens of photons, tunneling ionization creates ions in different excited states and even enables the formation of population inversion between ionic states. However, the underlying physics is still being debated. Here, we demonstrate a significant enhancement in the efficiency of multiphoton excitation when ionization of neutral molecules and resonant excitation of ions coexist in strong laser fields. It facilitates the dramatic increase in population inversion and lasing radiation in N_{2}^{+} around 1000nm pump wavelength. Utilizing the ionization-coupling theory, we discover that the synergistic interplay between tunneling ionization and multiphoton excitation enables the ionic coherence to be maximized by phase locking of the periodically created ionic dipoles and consistently maintain an optimal phase for the follow-up photoexcitation. This Letter provides new insights into the photoexcitation mechanism of ions in strong laser fields and opens up a route for optimizing ionic lasing radiations.

Nuclear momentum distributions governed by Rabi flopping in the dissociation of hydrogen molecular ions in strong laser fields

We study the Rabi flopping between the $1s{\ensuremath{\sigma}}_{g}$ and $2p{\ensuremath{\sigma}}_{u}$ states during the dissociation of hydrogen molecular ions in strong laser fields by numerically simulating the time-dependent Schr\"odinger equation. Starting either from a certain vibrational state or from coherently superimposed vibrational states weighted with Frank-Condon factors, the dissociative nuclear momentum distributions present multiple angular nodes and maxima due to molecular alignment-dependent Rabi flopping. The Rabi frequency and nuclear angular distribution depend on the laser chirp and laser ellipticity. Rabi flopping also determines the population on the $2p{\ensuremath{\sigma}}_{u}$ state and thus the dissociation probability. The deep understanding of Rabi flopping in molecular dissociation gives clues to control ultrafast molecular dynamics.

Controlling the collective radiative decay of molecular ions in strong laser fields

Molecular ions, produced via ultrafast ionization, can be quantum emitters with the aid of resonant electronic couplings, which makes them the ideal candidates to study strong-field quantum optics. In this work, we experimentally and numerically investigate the necessary condition for observing a collective emission arising from macroscopic quantum polarization in a population-inverted N 2 + gain system, uncovering how the individual ionic emitters proceed into a coherent collection within hundreds of femtoseconds. Our results show that for a relatively high-gain case, the collective emission behaviors can be readily initiated for all the employed triggering pulse area. However, for a low-gain case, the superradiant amplification is quenched since the building time of macroscopic interionic quantum coherence exceeds the dipole dephasing time, in which situation the seed amplification and free induction decay play an essential role. These findings not only clarify the contentious key issue regarding to the amplification mechanism of N 2 + lasing but also show the unique characteristics of ultrashort laser-induced amplification in a molecular ion system where both the microscopic and macroscopic quantum coherence might be present.

Three-electron correlations in strong laser field ionization.

Strong field processes involving several active electrons reveal unambiguous dynamical signatures of the Pauli principle importance even in the nonrelativistic regime. We exemplify this statement studying three active electrons model atoms interacting with strong pulsed radiation, using an ab-initio time-dependent Schrödinger equation on a grid. In our restricted dimensionality model we are able to analyze momenta correlations of the three outgoing electrons using Dalitz plots. The different symmetries of the electronic wavefunctions, directly related to the initial state spin components, appear clearly visible.

Ionization in intense laser fields beyond the electric dipole approximation: concepts, methods, achievements and future directions

The electric dipole approximation is widely used in atomic, molecular and optical physics and is typically related to a regime for which the wavelength is much larger than the atomic structure. However, studies have shown that in strong laser fields another regime exists where the dipole approximation breaks down. During the ionization process in intense laser fields and at long wavelengths the photoelectrons can reach higher velocities such that the magnetic field component of the laser field becomes significant. The ionization dynamics and the final momentum of the electron is therefore modified by the entire Lorentz force. In contrast the magnetic field interaction is neglected in the dipole approximation. Rapid developments in laser technology and advancements in the accuracy of the measurements techniques have enabled the observation of the influence of such non-dipole effects on the final angular photoelectron momentum distributions. More recently the number of studies on ionization beyond the dipole approximation has increased significantly, providing more important insight into fundamental properties of ionization processes. For example we have shown that the final three dimensional photoelectron momentum spectra is significantly affected by the non-dipole drift with the parent–ion interaction, the linear multiphoton momentum transfer on a sub-cycle time scale and the sharing of the transferred linear photon momenta between the electron and the ion. In this article we present an overview of the underlying mechanisms and we review the experimental techniques and the achievements in this field. We focus on ionization in strong laser fields in the regime where the dipole approximation is not valid but a fully relativistic description is not required.

Relativistic mask method for electron momentum distributions after ionization of hydrogen-like ions in strong laser fields

Wavefunction-splitting or mask method, widely used in the non-relativistic calculations of the photoelectron angular distributions, is extended to the relativistic domain within the dipole approximation. Since the closed-form expressions for the relativistic Volkov states are not available within the dipole approximation, we build such states numerically solving a single second-order differential equation. We calculate the photoelectron energy spectra and angular distributions for highly charged ions under different ionization regimes with both the direct and the relativistic mask methods. We show that the relativistic mask method works very well and reproduces the electron energy and angular distributions calculated by the direct method in the energy range where both methods can be used. On the other hand, the relativistic mask method can be applied for longer laser pulses and/or higher photoelectron energies where the direct method may have difficulties.

Isotope effects on the ionization of hydrogen molecular ions in strong laser fields

Isotope effects on the ionization of hydrogen molecular ions in strong laser fields are studied by numerically simulating the time-dependent Schr\odinger equation. Though the isotopes of hydrogen molecular ions have identical Born-Oppenheimer potential curves, the distinct ionization scenarios are observed for single-photon, multiphoton, and tunneling ionization. For multiphoton and tunneling ionization, the ionization rate of ${{\mathrm{H}}_{2}}^{+}$ is larger than that of ${{\mathrm{D}}_{2}}^{+}$ and ${{\mathrm{T}}_{2}}^{+}$. The ratio of the intensity-dependent tunneling ionization probabilities of ${{\mathrm{H}}_{2}}^{+}$ (${{\mathrm{D}}_{2}}^{+}$) and ${{\mathrm{T}}_{2}}^{+}$ can be qualitatively explained by the adiabatic tunneling theories if a few-femtosecond ultrashort pulse is used. For tens of femtosecond laser pulses, the nuclear movement is unavoidable and the time-dependent Schr\odinger equation simulation is necessary in order to calculate the ionization probability accurately. For single-photon ionization, the electron-nuclei joint energy spectra are distinct though the total ionization probabilities are similar. The elastic constant of potential curves can be retrieved by comparing the single-photon-induced electron-nuclei joint energy spectra of different isotopic molecular ions, which offers a potential technique to image molecules.

Pure even and odd harmonics produced in modeled hydrogen molecular ions in single-color strong laser fields

The even and odd high-order harmonic generation in a modeled hydrogen molecular ion in strong laser fields is studied by numerically simulating the time-dependent Schrodinger equation. By applying a linearly polarized laser pulse whose polarization axis is perpendicular to the molecular axis, the pure odd harmonics polarized along the laser polarization direction are produced. Meanwhile, the pure even harmonics polarized along the molecular axis may be produced simultaneously either by adding an extra weak direct-current electric field along the molecular axis, or by artificially setting asymmetric charges for the two nuclei. The Bohmian trajectories reveal that the pure even harmonics are contributed by the dipole formed by the asymmetric expansion of the ionized wave packet along the molecular axis, instead of the asymmetric Coulomb attraction for the rescattering electron as expected. Moreover, the relationship between the symmetry of molecular orbital and the parity of high-order harmonics is also explored.

Tunneling exits of in strong laser fields**Project supported by National Natural Science Foundation of China (Grant Nos. 11574205, 11327902, and 11421064), the Innovation Program of Shanghai Municipal Education Commission (Grant No. 2017-01-07-00-02-E00034).

Different from atoms, the multicenter of the Coulombic potentials in molecules makes the tunneling ionization complex, and the electron tunnels out the laser-dressed Coulomb potential with a complex structure. We study tunneling exits of at large internuclear distance in strong laser fields by numerically simulating the time-dependent Schrödinger equation plus a classical backward propagation of the ionized wave packet. This study strengthens the understanding of molecular tunneling ionization in strong laser fields.

Fraunhofer and refractive scattering of heavy ions in strong laser fields

Until recently the potential scattering of a charged particle in a laser field received attention exclusively in atomic physics. The differential cross-section of laser-assisted electron-atom collisions for n emitted or absorbed photons is provided by a simple law which casts the result as a product between the field-free value and the square of the Bessel function of order n with its argument containing the effect of the laser in a non-perturbative way. From the experimental standpoint, laser-assisted electron-atom collisions are important because they allow the observation of multiphoton effects even at moderate laser intensities. The aim of this study is to calculate the nucleus-nucleus differential cross section in the field of a strong laser with wavelengths in the optical domain such that the low-frequency approximation is fulfilled. We investigate the dependence of the n-photon differential cross-section on the intensity, photon energy and shape of the pulse for a projectile/target combination at a fixed collision energy which exhibits a superposition of Fraunhofer and refractive behavior. We also discuss the role of the laser perturbation on the near and farside decomposition in the angular distribution, an issue never discussed before in the literature. We apply a standard optical model approach to explain the experimental differential cross-section of the elastic scattering of 4He on 58Ni at a laboratory energy E = 139 MeV and resolve the corresponding farside/nearside (F/N) decomposition in the field-free case. We give an example of reaction in which Fraunhofer diffraction and refractive rainbow hump effects are easily recognized in the elastic angular distribution. Next, we apply the Kroll-Watson theorem, in order to determine the n -photon contributions to the cross-section for continuous-wave (cw) and modulated pulses. In the elastic scattering of heavy ions in a radiation field of low intensity, the amplitude drops by orders of magnitude with respect to the unperturbed case once the exchange of photons is initiated. For intensities approaching $I=10^{17}$ W/cm2 multiphoton effects become important. In the case of short laser pulses we conclude that the strength of n-photon contribution increases with the pulse duration.

Contribution of resonance excitation on ionization of OCS molecules in strong laser fields

Photoelectron images from single ionization of OCS molecules are measured at 800 nm or 400 nm linearly polarized laser pulses (∼50 fs) using velocity-map imaging techniques. The resonant ionization of the molecules has been studied by tracing the electron energy shift in the photoelectron energy spectra at different laser intensities, and the contributions of three excited states at certain laser intensities and wavelengths are identified. During the ionization of OCS molecules, two excited states (1Δ and 1∏) are shifted into resonance at different 800 nm laser intensities, and the Rydberg state 4pσ ∏ is involved in the resonance for a 400 nm laser. The demonstration of resonant excitation contribution experimentally will help further the understanding of OCS ionization in strong laser fields.

Excitation of Rydberg wave packets in the tunneling regime

In the tunneling regime for strong laser field ionization of atoms, experimental studies have shown that a substantial fraction of atoms survive the laser pulse in many Rydberg states. To explain the origin of such trapping of population into Rydberg states, two mechanisms have been proposed: the first involves ac-Stark-shifted multiphoton resonances, and the second, called frustrated tunneling ionization, leads to the recombination of tunneled electrons into Rydberg states. We use a very accurate spectral method based on complex Sturmian functions to solve the time-dependent Schr\odinger equation for hydrogen in a linearly polarized infrared pulse and to calculate the tunneling probability in terms of the atomic ground-state width. We examine the probability of excitation into Rydberg states as a function of the peak intensity for various pulse durations and two wavelengths, 800 and 1800 nm, and we try to explain the results in light of the two aforementioned mechanisms. For long pulses of 800 nm wavelength, the extreme sensitivity of the trapping of population into high-lying Rydberg states to the peak intensity, the well-defined value, and parity of the angular momentum of the populated Rydberg states and the presence of Freeman resonances can be explained using a multiphotonic excitation mechanism. For strong pulses of 1800 nm wavelength, in the so-called adiabatic or quasistatic tunneling regime, the oscillations of the excitation probability as a function of intensity are in phase opposition to the ionization probability, and we observe a migration toward high values of the angular momentum with different distributions in the angular momentum at the maxima and minima of the oscillations. We also present a detailed study of how the excited-state wave packet builds up in time during the interaction of the atom with the pulse.

Unified Time and Frequency Picture of Ultrafast Atomic Excitation in Strong Laser Fields.

Excitation and ionization in strong laser fields lies at the heart of such diverse research directions as high-harmonic generation and spectroscopy, laser-induced diffraction imaging, emission of femtosecond electron bunches from nanotips, self-guiding, filamentation and mirrorless lasing during propagation of light in atmospheres. While extensive quantum mechanical and semiclassical calculations on strong-field ionization are well backed by sophisticated experiments, the existing scattered theoretical work aiming at a full quantitative understanding of strong-field excitation lacks experimental confirmation. Here we present experiments on strong-field excitation in both the tunneling and multiphoton regimes and their rigorous interpretation by time dependent Schrödinger equation calculations, which finally consolidates the seemingly opposing strong-field regimes with their complementary pictures. Most strikingly, we observe an unprecedented enhancement of excitation yields, which opens new possibilities in ultrafast strong-field control of Rydberg wave packet excitation and laser intensity characterization.

Nonadiabatic Effect on the Rescattering Trajectories of Electrons in Strong Laser Field Ionization Process**Supported by the National Natural Science Foundation of China under Grant Nos 11425414 and 11504215, and the Scientific Research Training Program of Shanxi University.

The important features of the rescattering trajectories in strong field ionization process such as the cutoff of the return energy at 3.17UP and that of the final energy at 10UP are obtained, based on the adiabatic approximation in which the initial momentum of the electron is assumed to be zero. We theoretically study the nonadiabatic effect by assuming a nonzero initial momentum on the rescattering trajectories based on the semiclassical simpleman model. We show that the nonzero initial momentum will modify both the maximal return energy at collision and the final energy after backward scattering, but in different ways for odd and even number of return trajectories. The energies are increased for even number of returns but are decreased for odd number of returns when the nonzero (positive or negative) initial momentum is applied.

Population Redistribution Among Multiple Electronic States of Molecular Nitrogen Ions in Strong Laser Fields.

We carry out a combined theoretical and experimental investigation on the population distributions in the ground and excited states of tunnel-ionized nitrogen molecules at various driver wavelengths in the near- and midinfrared range. Our results reveal that efficient couplings (i.e., population exchanges) between the ground N_{2}^{+}(X^{2}Σ_{g}^{+}) state and the excited N_{2}^{+}(A^{2}Π_{u}) and N_{2}^{+}(B^{2}Σ_{u}^{+}) states occur in strong laser fields. The couplings result in a population inversion between the N_{2}^{+}(X^{2}Σ_{g}^{+}) and N_{2}^{+}(B^{2}Σ_{u}^{+}) states at wavelengths near 800nm, which is verified by our experimental observation of the amplification of a seed at ∼391 nm. The result provides insight into the mechanism of free-space nitrogen ion lasers generated in remote air with strong femtosecond laser pulses.

Fraunhofer-like diffracted lateral photoelectron momentum distributions ofH2+in charge-resonance-enhanced ionization in strong laser fields

Fraunhofer-like diffracted lateral photoelectron momentum distributions of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi mathvariant="normal">H</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:msup><mml:mrow /><mml:mo>+</mml:mo></mml:msup></mml:mrow></mml:math>in charge-resonance-enhanced ionization in strong laser fields

Ultrafast resolution of tunneling delay time

We compare the main competing theories of tunneling time against experimental measurements using the attoclock in strong laser field ionization of helium atoms. Refined attoclock measurements reveal a real and not instantaneous tunneling delay time over a large intensity regime, using two different experimental apparatus. Only two of the theoretical predictions are compatible within our experimental error: the Larmor time, and the probability distribution of tunneling times constructed using a Feynman Path Integral (FPI) formulation. The latter better matches the observed qualitative change in tunneling time over a wide intensity range, and predicts a broad tunneling time distribution with a long tail. The implication of such a probability distribution of tunneling times, as opposed to a distinct tunneling time, challenges how valence electron dynamics are currently reconstructed in attosecond science. It means that one must account for a significant uncertainty as to when the hole dynamics begin to evolve.

Direct detection of enhanced ionization in CO andN2in strong fields

Enhanced ionization (EI) of molecules has been extensively studied over the past two decades as a common process in molecular dissociative ionization in strong laser fields. Direct evidence for EI has been found only in ${\mathrm{I}}_{2}$ and ${\mathrm{H}}_{2}$. However, in this work we perform a direct study of EI in CO and ${\mathrm{N}}_{2}$, and find enhanced ionization in an alternate dissociation channel in each of these two molecules following double ionization. Surprisingly, EI does not happen in the commonly seen dissociation channels that were previously assigned undergoing EI. Instead, EI occurs only in the alternate channels seen here with a lower kinetic-energy release.

Time-resolved photodissociation of oxygen at 162 nm

Oxygen was excited by 10 fs pulses in the Schumann–Runge continuum at 162 nm, which is by 0.57 eV above the dissociation limit. It was probed by high-intensity ionization at 810 nm with 1014 W cm−2, measuring the ion yields. The O2+ signal decays in 4.3 fs, which is much shorter than the expected time for dissociation. It is ascribed to a rapid decay of the ionization probability. In a similar time, the ion in the second excited state (with excess energy taken over from the neutral) reaches the dissociation limit, whereas this time would be much longer from the two lower ion states. In fact, the O+ signal rises to a (first) maximum at 6 fs. The preference for the higher ion state is rationalized by an intermediate resonance in the neutral molecule for which the polarization dependence also provides evidence. But the shape of the O+ signal is very odd: it exhibits three maxima (at 6, 29 and 53 fs) of increasing intensity, before decaying rapidly (≤3.5 fs) to a pedestal. In contrast to the first maximum, the others appear at times when there is practically no interatomic force left in the excited state. We postulate a highly repulsive doubly excited state as a resonance for interpreting the second maximum, and for the third an ion-pair state lying further outside. Comparison is made with enhanced ionization, which has often been found at large interatomic distances on multiple ionization in strong laser fields. Consistent with this mechanism is the absence of similar observations at negative delay times, where five fundamental photons act as a pump and the fifth harmonic as a probe.

The RMT method for many-electron atomic systems in intense short-pulse laser light

We describe a new ab initio method for solving the time-dependent Schrödinger equation for multi-electron atomic systems exposed to intense short-pulse laser light. We call the method the R-matrix with time-dependence (RMT) method. Our starting point is a finite-difference numerical integrator (HELIUM), which has proved successful at describing few-electron atoms and atomic ions in strong laser fields with high accuracy. By exploiting the R-matrix division-of-space concept, we bring together a numerical method most appropriate to the multi-electron finite inner region (R-matrix basis set) and a different numerical method most appropriate to the one-electron outer region (finite difference). In order to exploit massively parallel supercomputers efficiently, we time-propagate the wavefunction in both regions by employing Arnoldi methods, originally developed for HELIUM.