Breakdown of the dipole approximation in strong-field ionization

Role of the Binding Energy on Nondipole Effects in Single-Photon Ionization

We experimentally study the influence of the binding energy on nondipole effects in K-shell single-photon ionization of atoms at high photon energies. We find that for each ionization event, as expected by momentum conservation, the photon momentum is transferred almost fully to the recoiling ion. The momentum distribution of the electrons becomes asymmetrically deformed along the photon propagation direction with a mean value of 8/(5c)(E_{γ}-I_{P}) confirming an almost 100 year old prediction by Sommerfeld and Schur [Ann. Phys. (N.Y.) 396, 409 (1930)10.1002/andp.19303960402]. The emission direction of the photoions results from competition between the forward-directed photon momentum and the backward-directed recoil imparted by the photoelectron. Which of the two counteracting effects prevails depends on the binding energy of the emitted electron. As an example, we show that at 20 keV photon energy, Ne^{+} and Ar^{+} photoions are pushed backward towards the radiation source, while Kr^{+} photoions are emitted forward along the light propagation direction.

Observation of Nondipole-Induced Asymmetry in the Angular Emission Distribution of Photoelectrons from Fixed-in-Space CO Molecules

We investigate experimentally and theoretically the C and O 1s photoionization of fixed-in-space CO molecules at a photon energy of 905 eV. We find a significant dependence of the photoelectron angular distributions on the direction of propagation of the ionizing radiation. It results from an interplay of nondipole effects, on one hand, and molecular effects, on the other. The nondipole effects lead to an increase of the emission probability in the forward direction along the light propagation, and the photoelectron wave being scattered by the molecular potential gives rise to a strong peak in the direction of the atom neighboring the emitter site. These effects can either conspire or extenuate each other, depending on the photoelectron emission direction and molecular orientation in space.

Nondipole Time Delay and Double-Slit Interference in Tunneling Ionization

Recently two-center interference in single-photon molecular ionization was employed to observe a zeptosecond time delay due to the photon propagation of the internuclear distance in a molecule [Grundmann et al., Science 370, 339 (2020)SCIEAS0036-807510.1126/science.abb9318]. We investigate the possibility of a comparable nondipole time delay in tunneling ionization and decode the emerged time delay signal. With the here newly developed Coulomb-corrected nondipole molecular strong-field approximation, we derive and analyze the photoelectron momentum distribution, the signature of nondipole effects, and the role of the degeneracy of the molecular orbitals. We show that the ejected electron momentum shifts and interference fringes efficiently imprint both the molecule structure and laser parameters. The corresponding nondipole time delay value significantly deviates from that in single-photon ionization. In particular, when the two-center interference in the molecule is destructive, the time delay is independent of the bond length. We also identify the double-slit interference in tunneling ionization of atoms with nonzero angular momentum via a nondipole momentum shift.

Increasing ion yield circular dichroism in femtosecond photoionisation using optimal control theory

We investigate how optimal control theory can be used to improve Circular Dichroism (CD) signals for the A-band of fenchone measured via the photoionization yield upon further excitation. These transitions are electric dipole forbidden to first order, which translates into low population transfer to the excited state but allows for a clearer interplay between electric and magnetic transition dipole moments, which are of the same order of magnitude. Using a model including the electronic ground and excited A state as well as all permanent and transition multipole moments up to the electric quadrupole, we find that the absolute CD signal of randomly oriented molecules can be increased by a factor of 2.5 when using shaped laser pulses, with the anisotropy parameter g increasing from 0.06 to 1. We find that this effect is caused by the interference between the excitation pathways prompted by the different multipole moments of the molecule.

Photoelectron energy peaks shift against the radiation pressure in strong-field ionization

The photoelectric effect describes the ejection of an electron upon absorption of one or several photons. The kinetic energy of this electron is determined by the photon energy reduced by the binding energy of the electron and, if strong laser fields are involved, by the ponderomotive potential in addition. It has therefore been widely taken for granted that for atoms and molecules, the photoelectron energy does not depend on the electron's emission direction, but theoretical studies have questioned this since 1990. Here, we provide experimental evidence that the energies of photoelectrons emitted against the light propagation direction are shifted toward higher values, while those electrons that are emitted along the light propagation direction are shifted to lower values. We attribute the energy shift to a nondipole contribution to the ponderomotive potential that is due to the interaction of the moving electrons with the incident photons.

Magnetic-Field Effect as a Tool to Investigate Electron Correlation in Strong-Field Ionization

The influence of the magnetic component of the driving electromagnetic field is often neglected when investigating light-matter interaction. We show that the magnetic component of the light field plays an important role in nonsequential double ionization, which serves as a powerful tool to investigate electron correlation. We investigate the magnetic-field effects in double ionization of xenon atoms driven by near-infrared ultrashort femtosecond laser pulses and find that the mean forward shift of the electron momentum distribution in light-propagation direction agrees well with the classical prediction, where no under-barrier or recollisional nondipole enhancement is observed. By extending classical trajectory Monte Carlo simulations beyond the dipole approximation, we reveal that double ionization proceeds via recollision-induced doubly excited states, followed by subsequent sequential over-barrier field ionization of the two electrons. In agreement with this model, the binding energies do not lead to an additional nondipole forward shift of the electrons. Our findings provide a new method to study electron correlation by exploiting the effect of the magnetic component of the electromagnetic field.

Magnetic-Field Effect in High-Order Above-Threshold Ionization

We experimentally and theoretically investigate the influence of the magnetic component of an electromagnetic field on high-order above-threshold ionization of xenon atoms driven by ultrashort femtosecond laser pulses. The nondipole shift of the electron momentum distribution along the light-propagation direction for high energy electrons beyond the 2U_{p} classical cutoff is found to be vastly different from that below this cutoff, where U_{p} is the ponderomotive potential of the driving laser field. A local minimum structure in the momentum dependence of the nondipole shift above the cutoff is identified for the first time. With the help of classical and quantum-orbit analysis, we show that large-angle rescattering of the electrons strongly alters the partitioning of the photon momentum between electron and ion. The sensitivity of the observed nondipole shift to the electronic structure of the target atom is confirmed by three-dimensional time-dependent Schrödinger equation simulations for different model potentials. Our work paves the way toward understanding the physics of extreme light-matter interactions at long wavelengths and high electron kinetic energies.

Recent Progress and Future Prospects on All-Organic Polymer Dielectrics for Energy Storage Capacitors

With the development of advanced electronic devices and electric power systems, polymer-based dielectric film capacitors with high energy storage capability have become particularly important. Compared with polymer nanocomposites with widespread attention, all-organic polymers are fundamental and have been proven to be more effective choices in the process of scalable, continuous, and large-scale industrial production, leading to many dielectric and energy storage applications. In the past decade, efforts have intensified in this field with great progress in newly discovered dielectric polymers, fundamental production technologies, and extension toward emerging computational strategies. This review summarizes the recent progress in the field of energy storage based on conventional as well as heat-resistant all-organic polymer materials with the focus on strategies to enhance the dielectric properties and energy storage performances. The key parameters of all-organic polymers, such as dielectric constant, dielectric loss, breakdown strength, energy density, and charge-discharge efficiency, have been thoroughly studied. In addition, the applications of computer-aided calculation including density functional theory, machine learning, and materials genome in rational design and performance prediction of polymer dielectrics are reviewed in detail. Based on a comprehensive understanding of recent developments, guidelines and prospects for the future development of all-organic polymer materials with dielectric and energy storage applications are proposed.

Quantum battles in attoscience: tunnelling

ABSTRACT

What is the nature of tunnelling? This yet unanswered question is as pertinent today as it was at the dawn of quantum mechanics. This article presents a cross section of current perspectives on the interpretation, computational modelling, and numerical investigation of tunnelling processes in attosecond physics as debated in the Quantum Battles in Attoscience virtual workshop 2020.

GRAPHIC ABSTRACT

Exploring spin symmetry-breaking effects for static field ionization of atoms: Is there an analog to the Coulson-Fischer point in bond dissociation?

Löwdin's symmetry dilemma is an ubiquitous issue in approximate quantum chemistry. In the context of Hartree-Fock (HF) theory, the use of Slater determinants with some imposed constraints to preserve symmetries of the exact problem may lead to physically unreasonable potential energy surfaces. On the other hand, lifting these constraints leads to the so-called broken symmetry solutions that usually provide better energetics, at the cost of losing information about good quantum numbers that describe the state of the system. This behavior has previously been extensively studied in the context of bond dissociation. This paper studies the behavior of different classes of HF spin polarized solutions (restricted, unrestricted, and generalized) in the context of ionization by strong static electric fields. We find that, for simple two electron systems, unrestricted Hartree-Fock (UHF) is able to provide a qualitatively good description of states involved during the ionization process (neutral, singly ionized, and doubly ionized states), whereas RHF fails to describe the singly ionized state. For more complex systems, even though UHF is able to capture some of the expected characteristics of the ionized states, it is constrained to a single M_s (diabatic) manifold in the energy surface as a function of field intensity. In this case, a better qualitative picture can be painted by using generalized Hartree-Fock as it is able to explore different spin manifolds and follow the lowest solution due to lack of collinearity constraints on the spin quantization axis.

Distribution of absorbed photons in the tunneling ionization process

We describe a procedure that allows us to solve the three-dimensional time-dependent Schrödinger equation for an atom interacting with a quantized one-mode electromagnetic field. Atom-field interaction is treated in an ab initio way prescribed by quantum electrodynamics. We use the procedure to calculate probability distributions of absorbed photons in the regime of tunneling ionization. We analyze evolution of the reduced photon density matrix describing the state of the field. We show that non-diagonal density matrix elements decay quickly, as a result of the decoherence process. A stochastic model, viewing ionization as a Markovian birth-death process, reproduces the main features of the calculated photon distributions.

Theory of Subcycle Linear Momentum Transfer in Strong-Field Tunneling Ionization

Interaction of a strong laser pulse with matter transfers not only energy but also linear momentum of the photons. Recent experimental advances have made it possible to detect the small amount of linear momentum delivered to the photoelectrons in strong-field ionization of atoms. We present numerical simulations as well as an analytical description of the subcycle phase (or time) resolved momentum transfer to an atom accessible by an attoclock protocol. We show that the light-field-induced momentum transfer is remarkably sensitive to properties of the ultrashort laser pulse such as its carrier-envelope phase and ellipticity. Moreover, we show that the subcycle-resolved linear momentum transfer can provide novel insights into the interplay between nonadiabatic and nondipole effects in strong-field ionization. This work paves the way towards the investigation of the so-far unexplored time-resolved nondipole nonadiabatic tunneling dynamics.

Observation of Photoion Backward Emission in Photoionization of He and N_{2}

We experimentally investigate the effects of the linear photon momentum on the momentum distributions of photoions and photoelectrons generated in one-photon ionization in an energy range of 300  eV≤E_{γ}≤40  keV. Our results show that for each ionization event the photon momentum is imparted onto the photoion, which is essentially the system's center of mass. Nevertheless, the mean value of the ion momentum distribution along the light propagation direction is backward-directed by -3/5 times the photon momentum. These results experimentally confirm a 90-year-old prediction.

Dissecting Strong-Field Excitation Dynamics with Atomic-Momentum Spectroscopy

Observation of internal quantum dynamics relies on correlations between the system being observed and the measurement apparatus. We propose using the c.m. degrees of freedom of atoms and molecules as a "built-in" monitoring device for observing their internal dynamics in nonperturbative laser fields. We illustrate the idea on the simplest model system-the hydrogen atom in an intense, tightly focused infrared laser beam. To this end, we develop a numerically tractable, quantum-mechanical treatment of correlations between internal and c.m. dynamics. We show that the transverse momentum records the time excited states experience the field, allowing femtosecond reconstruction of the strong-field excitation process. The ground state becomes weak-field seeking, an unambiguous and long sought-for signature of the Kramers-Henneberger regime.

Mapping initial transverse momenta of tunnel-ionized electrons to rescattering double ionization in nondipole regimes

We investigate the double ionization of a model Neon atom in strong middle infrared laser pulses by simulating the classical trajectories of the electron ensemble. After one electron tunnels out from the laser-dressed Coulomb barrier, it might undergo different returning trajectories depending on its initial transverse momentum, which in this wavelength may propagate along or deviate from the polarization direction. This initial transverse momentum determines the rescattering time, and thus some trajectories can have returning time longer than one optical cycle. These late-returning trajectories determine the correlated electron-electron momentum distribution for double ionization and allow us to disentangle each double ionization event from the final momentum distribution. The description of these trajectories allow us also to understand how the nondipole effects modify the correlated electron-electron momentum distribution in double ionization.

Attosecond timing of the dynamical Franz–Keldysh effect

To what extent do intra- or inter-band transitions dominate the optical response of dielectrics when pumped by a few-cycle near-infrared transient electric field? In order to find an answer to this question we investigate the dynamical Franz–Keldysh effect in polycrystalline diamond and discuss in detail the attosecond delay of the induced electron dynamics with regard to the driving transient electric field while the peak intensity is varied between 1 × 1012 and 10 × 1012 W cm−2. We found that the main oscillating feature in transient absorption at 43 eV is in phase with the electric field of the pump, to within 49 ± 78 as. However, the phase delay shows a slightly asymmetric V-shaped linear energy dispersion with a rate of about 200 as eV–1. Theoretical calculations within the dipole approximation reproduce the data and allow us to conclude that intra-band motion dominates under our experimental conditions.

It is all about phases: ultrafast holographic photoelectron imaging

Photoelectron holography constitutes a powerful tool for the ultrafast imaging of matter, as it combines high electron currents with subfemtosecond resolution, and gives information about transition amplitudes and phase shifts. Similarly to light holography, it uses the phase difference between the probe and the reference waves associated with qualitatively different ionization events for the reconstruction of the target and for ascertaining any changes that may occur. These are major advantages over other attosecond imaging techniques, which require elaborate interferometric schemes in order to extract phase differences. For that reason, ultrafast photoelectron holography has experienced a huge growth in activity, which has led to a vast, but fragmented landscape. The present review is an organizational effort towards unifying this landscape. This includes a historic account in which a connection with laser-induced electron diffraction is established, a summary of the main holographic structures encountered and their underlying physical mechanisms, a broad discussion of the theoretical methods employed, and of the key challenges and future possibilities. We delve deeper in our own work, and place a strong emphasis on quantum interference, and on the residual Coulomb potential.

Attosecond-Scale Streaking Methods for Strong-Field Ionization by Tailored Fields

Streaking with a weak probe field is applied to ionization in a two-dimensional strong field tailored to mimic linear polarization, but without disturbance by recollision or intracycle interference. This facilitates the observation of electron-momentum-resolved times of ionization with few-attosecond precision, as demonstrated by simulations for a model helium atom. Aligning the probe field along the ionizing field provides meaningful ionization times in agreement with the attoclock concept that ionization at maximum field corresponds to the peak of the momentum distribution, which is shifted due to the Coulomb force on the outgoing electron. In contrast, this attoclock shift is invisible in orthogonal streaking. Even without a probe field, streaking happens naturally along the laser propagation direction due to the laser magnetic field. As with an orthogonal probe field, the attoclock shift is not accessible by the magnetic-field scheme. For a polar molecule, the attoclock shift depends on orientation, but this does not imply an orientation dependence in ionization time.

Sub-cycle time resolution of multi-photon momentum transfer in strong-field ionization

During multi-photon ionization of an atom it is well understood how the involved photons transfer their energy to the ion and the photoelectron. However, the transfer of the photon linear momentum is still not fully understood. Here, we present a time-resolved measurement of linear momentum transfer along the laser pulse propagation direction. We can show that the linear momentum transfer to the photoelectron depends on the ionization time within the laser cycle using the attoclock technique. We can mostly explain the measured linear momentum transfer within a classical model for a free electron in a laser field. However, corrections are required due to the parent-ion interaction and due to the initial momentum when the electron enters the continuum. The parent-ion interaction induces a negative attosecond time delay between the appearance in the continuum of the electron with minimal linear momentum transfer and the point in time with maximum ionization rate.

Relativistic Nondipole Effects in Strong-Field Atomic Ionization at Moderate Intensities

We present a detailed experimental and theoretical study on the relativistic nondipole effects in strong-field atomic ionization by near-infrared linearly polarized few-cycle laser pulses in the intensity range of 10^{14}-10^{15}  W/cm^{2}. We record high-resolution photoelectron momentum distributions of argon using a reaction microscope and compare our measurements with a truly ab initio fully relativistic 3D model based on the time-dependent Dirac equation. We observe counterintuitive peak shifts of the transverse electron momentum distribution in the direction opposite to that of laser propagation as a function of laser intensity and demonstrate an excellent agreement between the experimental results and theoretical predictions.

An intense, few-cycle source in the long-wave infrared

For the last several decades, the wavelength range accessible for strong-field, few-cycle studies has remained limited to the visible, near infrared and mid-wave infrared regimes. In particular, sources in the long-wave infrared have been lacking. We report the development of a 1 kHz, few-cycle laser source with up to a 9 μm central wavelength and gigawatt peak powers. When focused, this source can ionize gas targets, which we demonstrate here through the ionization of atomic xenon at wavelengths ranging from 5 μm to 9 μm. This opens up new opportunities for fundamental atomic and molecular physics, enabling experimental tests of strong-field ionization theories in the extreme long-wavelength, few-cycle limit and the direct excitation of vibrational transitions in organic molecules.

Enhanced Strong Interaction between Nanocavities and p-shell Excitons Beyond the Dipole Approximation

Large coupling strengths in exciton-photon interactions are important for the quantum photonic network, while strong cavity-quantum dot interactions have been focused on s-shell excitons with small coupling strengths. Here we demonstrate strong interactions between cavities and p-shell excitons with a great enhancement by the in situ wave-function control. The p-shell excitons are demonstrated with much larger wave-function extents and nonlocal interactions beyond the dipole approximation. Then the interaction is tuned from the nonlocal to the local regime by the wave function shrinking, during which the enhancement is obtained. A large coupling strength of 210  μeV has been achieved, indicating the great potential of p-shell excitons for coherent information exchange. Furthermore, we propose a distributed delay model to quantitatively explain the coupling strength variation, revealing the intertwining of excitons and photons beyond the dipole approximation.

Symmetry breakdown of electron emission in extreme ultraviolet photoionization of argon

Short wavelength free-electron lasers (FELs), providing pulses of ultrahigh photon intensity, have revolutionized spectroscopy on ionic targets. Their exceptional photon flux enables multiple photon absorptions within a single femtosecond pulse, which in turn allows for deep insights into the photoionization process itself as well as into evolving ionic states of a target. Here we employ ultraintense pulses from the FEL FERMI to spectroscopically investigate the sequential emission of electrons from gaseous, atomic argon in the neutral as well as the ionic ground state. A pronounced forward-backward symmetry breaking of the angularly resolved emission patterns with respect to the light propagation direction is experimentally observed and theoretically explained for the region of the Cooper minimum, where the asymmetry of electron emission is strongly enhanced. These findings aim to originate a better understanding of the fundamentals of photon momentum transfer in ionic matter.

Limit on Excitation and Stabilization of Atoms in Intense Optical Laser Fields

Atomic excitation in strong optical laser fields has been found to take place even at intensities exceeding saturation. The concomitant acceleration of the atom in the focused laser field has been considered a strong link to, if not proof of, the existence of the so-called Kramers-Henneberger (KH) atom, a bound atomic system in an intense laser field. Recent findings have moved the importance of the KH atom from being purely of theoretical interest toward real world applications; for instance, in the context of laser filamentation. Considering this increasing importance, we explore the limits of strong-field excitation in optical fields, which are basically imposed by ionization through the spatial field envelope and the field propagation.

Photoemission and photoionization time delays and rates

Ionization and, in particular, ionization through the interaction with light play an important role in fundamental processes in physics, chemistry, and biology. In recent years, we have seen tremendous advances in our ability to measure the dynamics of photo-induced ionization in various systems in the gas, liquid, or solid phase. In this review, we will define the parameters used for quantifying these dynamics. We give a brief overview of some of the most important ionization processes and how to resolve the associated time delays and rates. With regard to time delays, we ask the question: how long does it take to remove an electron from an atom, molecule, or solid? With regard to rates, we ask the question: how many electrons are emitted in a given unit of time? We present state-of-the-art results on ionization and photoemission time delays and rates. Our review starts with the simplest physical systems: the attosecond dynamics of single-photon and tunnel ionization of atoms in the gas phase. We then extend the discussion to molecular gases and ionization of liquid targets. Finally, we present the measurements of ionization delays in femto- and attosecond photoemission from the solid-vacuum interface.

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.

Challenges in Simulating Light-Induced Processes in DNA

In this contribution, we give a perspective on the main challenges in performing theoretical simulations of photoinduced phenomena within DNA and its molecular building blocks. We distinguish the different tasks that should be involved in the simulation of a complete DNA strand subject to UV irradiation: (i) stationary quantum chemical computations; (ii) the explicit description of the initial excitation of DNA with light; (iii) modeling the nonadiabatic excited state dynamics; (iv) simulation of the detected experimental observable; and (v) the subsequent analysis of the respective results. We succinctly describe the methods that are currently employed in each of these steps. While for each of them, there are different approaches with different degrees of accuracy, no feasible method exists to tackle all problems at once. Depending on the technique or combination of several ones, it can be problematic to describe the stacking of nucleobases, bond breaking and formation, quantum interferences and tunneling or even simply to characterize the involved wavefunctions. It is therefore argued that more method development and/or the combination of different techniques are urgently required. It is essential also to exercise these new developments in further studies on DNA and subsystems thereof, ideally comprising simulations of all of the different components that occur in the corresponding experiments.

Lorentz drift compensation in high harmonic generation in the soft and hard X-ray regions of the spectrum

We present a semi-classical study of the effects of the Lorentz force on electrons during high harmonic generation in the soft and hard X-ray regions driven by near- and mid-infrared lasers with wavelengths from 0.8 to 20 μm, and at intensities below 10¹⁵ W/cm². The transverse extent of the longitudinal Lorentz drift is compared for both Gaussian focus and waveguide geometries. Both geometries exhibit a longitudinal electric field component that cancels the magnetic Lorentz drift in some regions of the focus, once each full optical cycle. We show that the Lorentz force contributes a super-Gaussian scaling which acts in addition to the dominant high harmonic flux scaling of λ^-(5-6) due to quantum diffusion. We predict that the high harmonic yield will be reduced for driving wavelengths > 6 μm, and that the presence of dynamic spatial mode asymmetries results in the generation of both even and odd harmonic orders. Remarkably, we show that under realistic conditions, the recollision process can be controlled and does not shut off completely even for wavelengths >10 μm and recollision energies greater than 15 keV.

Tunneling Time and Weak Measurement in Strong Field Ionization

Tunneling delays represent a hotly debated topic, with many conflicting definitions and little consensus on when and if such definitions accurately describe the physical observables. Here, we relate these different definitions to distinct experimental observables in strong field ionization, finding that two definitions, Larmor time and Bohmian time, are compatible with the attoclock observable and the resonance lifetime of a bound state, respectively. Both of these definitions are closely connected to the theory of weak measurement, with Larmor time being the weak measurement value of tunneling time and Bohmian trajectory corresponding to the average particle trajectory, which has been recently reconstructed using weak measurement in a two-slit experiment [S. Kocsis, B. Braverman, S. Ravets, M. J. Stevens, R. P. Mirin, L. K. Shalm, and A. M. Steinberg, Science 332, 1170 (2011)]. We demonstrate a big discrepancy in strong field ionization between the Bohmian and weak measurement values of tunneling time, and we suggest this arises because the tunneling time is calculated for a small probability postselected ensemble of electrons. Our results have important implications for the interpretation of experiments in attosecond science, suggesting that tunneling is unlikely to be an instantaneous process.

Exploring laser-driven quantum phenomena from a time-frequency analysis perspective: a comprehensive study

Time-frequency (TF) analysis is a powerful tool for exploring ultrafast dynamics in atoms and molecules. While some TF methods have demonstrated their usefulness and potential in several quantum systems, a systematic comparison among them is still lacking. To this end, we compare a series of classical and contemporary TF methods by taking hydrogen atom in a strong laser field as a benchmark. In addition, several TF methods such as Cohen class distribution other than the Wigner-Ville distribution, reassignment methods, and the empirical mode decomposition method are first introduced to exploration of ultrafast dynamics. Among these TF methods, the synchrosqueezing transform successfully illustrates the physical mechanisms in the multiphoton ionization regime and in the tunneling ionization regime. Furthermore, an empirical procedure to analyze an unknown complicated quantum system is provided, suggesting the versatility of TF analysis as a new viable venue for exploring quantum dynamics.

Characterization of Molecular Breakup by Very Intense Femtosecond XUV Laser Pulses

We study the breakup of H2+ exposed to superintense, femtosecond laser pulses with frequencies greater than that corresponding to the ionization potential. By solving the time-dependent Schrödinger equation in an extensive field parameter range, it is revealed that highly nonresonant dissociation channels can dominate over ionization. By considering field-dressed Born-Oppenheimer potential energy curves in the reference frame following a free electron in the field, we propose a simple physical model that characterizes this dissociation mechanism. The model is used to predict control of vibrational excitation, magnitude of the dissociation yields, and nuclear kinetic energy release spectra. Finally, the joint energy spectrum for the ionization process illustrates the energy sharing between the electron and the nuclei and the correlation between ionization and dissociation processes.