Strong-field Ionization Processes Research Articles

Joint probability calculation of the lateral velocity distribution in strong field ionization process

We describe an approach to the description of the time-development of the process of strong field ionization of atoms based on the calculation of the joint probability of occurrence of two events, event B being finding atom in the ionized state after the end of the laser pulse, event A being finding a particular value of a given physical observable at a moment of time inside the laser pulse duration. As an example of such an physical observable we consider lateral velocity component of the electron’s velocity. Our approach allows us to study time-evolution of the lateral velocity distribution for the ionized electron during the interval of the laser pulse duration. We present results of such a study for the cases of target atomic systems with short range Yukawa and Coulomb interactions.

High-order above-threshold ionization by a few-cycle laser pulse in the presence of a terahertz pulse

In our recent letter [D. B. Milo\ifmmode \check{s}\else \v{s}\fi{}evi\ifmmode \acute{c}\else \'{c}\fi{}, Opt. Lett. 47, 1669 (2022)] we proposed to apply a terahertz pulse to modify the ionization process induced by a strong midinfrared laser pulse. If the vector potentials of the laser and THz fields are comparable, the yield and the maximum energy of the photoelectrons emitted in the strong-field ionization process can be significantly increased. The time delay $\mathrm{\ensuremath{\Delta}}t$ between the THz pulse and the laser pulse is used as a control parameter. In the present work we further analyze this process, with particular emphasis on high-order above-threshold ionization (HATI). Using our improved strong-field approximation we calculate the ionization amplitude by numerical integration over the electron's ionization and travel times. We apply the quantum-orbit theory and the modified saddle-point method to provide a physical explanation. In addition to the previously considered ionization of Cs atoms by a 3100-nm midinfrared laser, we now show that qualitatively similar results can be obtained for HATI of Ar atoms by a much stronger 800-nm laser pulse. Furthermore, for HATI of Ar by a 3100-nm laser, assisted by a THz pulse of a few-MV/cm strength, we show that the photoelectron energy can be in the keV region.

Multiphoton process investigation in silica by UV femtosecond laser

We investigated the interaction processes between high intensity femtosecond ultraviolet laser pulses and amorphous silica, leading to permanent refractive-index changes that are at the basis of advanced manufacturing for photonics devices. The experiment, carried out as a function of the laser power, improves our understanding on the strong-field ionization process by the monitoring of the 1.9 eV and 2.65 eV emissions, related to nonbridging oxygen hole centers and self-trapped exciton, respectively, induced in the exposed glass region. Our results clearly proved that the UV laser light band-to-band absorption is allowed in the multiphoton ionization limit, whose consecutive relaxation leads to the generation of these photoluminescence (PL) signatures. Furthermore, we coupled the online PL investigation with post mortem analysis of the irradiated volume through phase contrast microscopy, Raman and steady state PL, providing a complete view of the silica-femtosecond laser interaction.

Partial-wave representation of the strong-field approximation

The strong-field approximation (SFA) has been widely applied to model ionization processes in short and intense laser pulses. Several approaches have been suggested in order to overcome certain limitations of the original SFA formulation with regard to the representation of the initial bound and final continuum states of the emitted electron as well as a suitable description of the driving laser pulse. We here present a reformulation of the SFA in terms of partial waves and spherical tensor operators that supports a quite simple implementation and the comparison of different treatments of the active (photo)electron and the laser pulses. In particular, this reformulation helps to adapt the SFA to experimental setups, and it paves the way to extend the strong-field theory toward the study of nondipole contributions in light-atom interactions as well as of many-particle correlations in strong-field ionization processes. A series of detailed computations have been carried out in order to confirm the validity of the reformulation and to show how the representation of the bound and continuum states affects the predicted above-threshold ionization spectra and related observables.

Ellipticity-dependent sequential over-barrier ionization of cold rubidium

We perform high-resolution measurements of momentum distribution on Rb$^{n+}$ recoil ions up to charge state $n=4$, where laser-cooled rubidium atoms are ionized by femtosecond elliptically polarized lasers with the pulse duration of 35 fs and the intensity of 3.3$\times$10$^{15}$ W/cm$^2$ in the over-barrier ionization (OBI) regime. The momentum distributions of the recoil ions are found to exhibit multi-band structures as the ellipticity varies from the linear to circular polarizations. The origin of these band structures can be explained quantitatively by the classical OBI model and dedicated classical trajectory Monte Carlo simulations with Heisenberg potential. Specifically, with back analysis of the classical trajectories, we reveal the ionization time and the OBI geometry of the sequentially released electrons, disentangling the mechanisms behind the tilted angle of the band structures. These results indicate that the classical treatment can describe the strong-field multiple ionization processes of alkali atoms.

Laser polarization dependence of strong-field ionization in lithium niobate

Laser micromachining techniques using femtosecond laser pulses are employed for the fabrication of a wide range of devices, from optical waveguides and fiber Bragg gratings to microfluidic systems. In this perspective, it is important to characterize how transparent materials respond to the high-intensity laser field in order to fully understand and control the strong-field ionization process at the core of such techniques. Here, we characterize the laser polarization dependence of $y$-cut and $x$-cut ferroelectric lithium niobate (${\mathrm{LiNbO}}_{3}$) upon ionization. Using linearly polarized 1800-nm femtosecond pulses, we perform single-shot laser-induced ablation measurements to obtain a macroscopic observable with a large contrast compared to all-optical techniques. In the tunnel ionization regime, the crystal orientation can be correlated with the structural symmetry/asymmetry of the material. This is revealed through a variation of the ablated area when the laser polarization is rotated with respect to the $c$ axis of the crystal. It is further found that ablation is more pronounced when the laser polarization is oriented towards angular regions containing Nb-O bonds of the unit cell, identifying the main chemical bonds contributing to the ionization of the material. The experimental results are supported by numerical simulations based on a two-band model for ${\mathrm{LiNbO}}_{3}$.

Strong-field control and attosecond probing of multielectron dynamics

The past thirty years witnessed rapid developing of strong field physics that leads to the first generation of attosecond (10−18 s) pulses. The duration of available pulses has recently been reduced to less than 100 as, approaching the Kepler period of a classical electron revolving around the nucleus. For the first time, electron motions inside atoms, molecules and solids can be traced, probed and even steered in real time. It pushed the study on ultrafast dynamic processes into a new frontier, giving birth to attosecond physics. The development of attosecond pulses provides unprecedented coherent ultrashort XUV (extreme ultra-violet) of soft X-ray sources that enable imaging the atomic structure and resolving the related quantum dynamics for matter science. In particular, it allows the probing and monitoring of electron dynamics in the natural time scale of attoseconds with atomic spatial resolution. The generation and applications of attosecond pulses are directly related to the control and manipulation of the sub-cycle electron dynamics. Recent studies on the correlated multielectron dynamics have provided insight into the optical and dynamical properties of matter in the perspectives of time, phase and entanglement. It deepens our understanding on some of the fundamental questions, e.g., how the single or multiple photons are absorbed and how short are the quantum processes such as photoionization, tunneling ionization and charge migration. Although currently attosecond pulses are limited by the flux and pulse duration, the combination of attosecond pulses with intense infrared laser pulses paves new ways of controlling and probing electron dynamics in the domains of energy, time and space that lays the foundation for petahertz optoelectronics and attosecond pulse based transient spectroscopy. In this review, we will first briefly summarize the advancement of strong field and ultrafast physics including the relevant experimental findings, the theoretical explorations, the related technologies and the possible applications. Then we focus on the sub-cycle electron or multielectron dynamics and their manifestation on the ionization and coherent radiation properties. We start with the time behavior of Fano resonance and how it can be probed in time domain. In section 2, the correlated electron dynamics is discussed in term of anti-screening effect and Pauli effect that influence strong field ionization and high harmonic generation processes. In section 3, the coherent emission with frequency from terahertz to soft XUV and their joint measurement are discussed by emphasizing the generation mechanism of terahertz wave in two-color laser pulses. The developed high-harmonic and terahertz wave spectroscopy (HATS) is shown capable of imaging the molecular structure and dynamics. In section 4, the time-resolving of electron and hole dynamics and their coherence is proposed based on attosecond transient absorption technique. The coherence of ionization and the correlated electron dynamics is hinted crucial for electron-hole interaction. The topics are very limited and mainly selected from the perspectives of our group.

Entropy-based view of the strong field ionization process

We apply information theoretic entropies of coordinate and velocity distributions in quantum mechanics for the description of the strong field ionization process. The approach is based on the properties of the entropies used in the information theory, viz., their ability to gauge the ‘distance’ between the probability distributions and thus to be sensitive to the distributions variations. Study of the entropies as functions of time allows thus to visualize conveniently evolution of the wave-function of the system undergoing strong field ionization, and to pin down, in particular, the times when the wave-function begins to change appreciably.

Direct probing of tunneling time in strong-field ionization processes by time-dependent wave packets.

We propose a straightforward approach to directly probe the tunneling time by observing the transition of photoelectron wave packets in strong-field ionization processes, where Coulomb potentials do not affect the results. A circularly polarized laser pulse is used to avoid the impact of scattering electrons on the direct ionization electrons, and a pure transmission photoelectron wave packet can be obtained. Then, a positive tunneling time is extracted. The results demonstrate that the tunneling time is dominated mainly by the laser frequency in some laser intensity range. At the same time, we also investigate the tunneling time by analyzing the instantaneous ionization rate, and the consentaneous results are obtained.

Dissociative frustrated multiple ionization of hydrogen chloride in intense femtosecond laser fields

The dissociative frustrated multiple ionization of hydrogen chloride (HCl) molecules in intense femtosecond laser fields is investigated by employing the coincidence measurement technique in cold target recoil ion momentum spectroscopy. Various dissociative frustrated multiple ionization channels caused by populating one or two electrons to highly excited Rydberg states can be clearly distinguished for HCl in linearly polarized intense laser fields. The excited charged fragmentations, depending on their occupied principle quantum numbers, can be either directly identified forming a ``knee'' structure in the kinetic energy release spectrum, or singly ionized by the weak electric field in the spectrometer, or by blackbody radiation after the conclusion of the laser pulse. The inherent feature of the potential energy curves of HCl plays an important role in the strong-field dissociative frustrated multiple ionization process.

Interplay between Coulomb-focusing and non-dipole effects in strong-field ionization with elliptical polarization

We study strong-field ionization and rescattering beyond the long-wavelength limit of the dipole approximation with elliptically polarized mid-IR laser pulses. Full three-dimensional photoelectron momentum distributions (PMDs) measured with velocity map imaging and tomographic reconstruction revealed an unexpected sharp ridge structure in the polarization plane (2018 Phys. Rev. A 97 013404). This thin line-shaped ridge structure for low-energy photoelectrons is correlated with the ellipticity-dependent asymmetry of the PMD along the beam propagation direction. The peak of the projection of the PMD onto the beam propagation axis is shifted from negative to positive values when the sharp ridge fades away with increasing ellipticity. With classical trajectory Monte Carlo simulations and analytical analysis, we study the underlying physics of this feature. The underlying physics is based on the interplay between the lateral drift of the ionized electron, the laser magnetic field induced drift in the laser propagation direction, and Coulomb focusing. To apply our observations to emerging techniques relying on strong-field ionization processes, including time-resolved holography and molecular imaging, we present a detailed classical trajectory-based analysis of our observations. The analysis leads to the explanation of the fine structure of the ridge and its non-dipole behavior upon rescattering while introducing restrictions on the ellipticity. These restrictions as well as the ionization and recollision phases provide additional observables to gain information on the timing of the ionization and recollision process and non-dipole properties of the ionization process.

Virtual detector theory for strong-field atomic ionization

A virtual detector (VD) is an imaginary device located at a fixed position in space that extracts information from the wave packet passing through it. By recording the particle momentum and the corresponding probability current at each time, the VDs can accumulate and build the differential momentum distribution of the particle, in a way that resembles real experiments. A mathematical proof is given for the equivalence of the differential momentum distribution obtained by the VD method and by Fourier transforming the wave function. In addition to being a tool for reducing the computational load, VDs have also been found useful in interpreting the ultrafast strong-field ionization process, especially the controversial quantum tunneling process.

Velocity map imaging of scattering dynamics in orthogonal two-color fields

In strong-field ionization processes, two-color laser fields are frequently used for controlling sub-cycle electron dynamics via the relative phase of the laser fields. Here we apply this technique to velocity map imaging spectroscopy using an unconventional orientation with the polarization of the ionizing laser field perpendicular to the detector surface and the steering field parallel to it. This geometry allows not only to image the phase-dependent photoelectron momentum distribution (PMD) of low-energy electrons that interact only weakly with the ion (direct electrons), but also to investigate the low yield of higher-energy rescattered electrons. Phase-dependent measurements of the PMD of neon and xenon demonstrate control over direct and rescattered electrons. The results are compared with semi-classical calculations in three dimensions including elastic scattering at different orders of return and with solutions of the three-dimensional time-dependent Schrödinger equation.

State-resolved attosecond reversible and irreversible dynamics in strong optical fields

Strong-field ionization (SFI) is a key process for accessing real-time quantum dynamics of electrons on the attosecond timescale. The theoretical foundation of SFI was pioneered in the 1960s, and later refined by various analytical models. While asymptotic ionization rates predicted by these models have been tested to be in reasonable agreement for a wide range of laser parameters, predictions for SFI on the sub-laser-cycle timescale are either beyond the scope of the models or show strong qualitative deviations from full quantum-mechanical simulations. Here, using the unprecedented state specificity of attosecond transient absorption spectroscopy, we follow the real-time SFI process of the two valence spin–orbit states of xenon. The results reveal that the irreversible tunnelling contribution is accompanied by a reversible electronic population that exhibits an observable spin–orbit-dependent phase delay. A detailed theoretical analysis attributes this observation to transient ground-state polarization, an unexpected facet of SFI that cannot be captured by existing analytical models that focus exclusively on the production of asymptotic electron/ion yields. An experimental and theoretical study of the real-time dynamics in strong-field ionization of xenon atoms reveals the previously unknown role of transient ground-state polarization.

Exit point in the strong field ionization process

We analyze the process of strong field ionization using the Bohmian approach. This allows retention of the concept of electron trajectories. We consider the tunnelling regime of ionization. We show that, in this regime, the coordinate distribution for the ionized electron has peaks near the points in space that can be interpreted as exit points. The interval of time during which ionization occurs is marked by a quick broadening of the coordinate distribution. The concept of the exit point in the tunneling regime, which has long been assumed for the description of strong field ionization, is justified by our analysis.

Atomic processes in bicircular fields

Various laser-induced and laser-assisted processes in atoms exposed to bicircular fields are investigated. The strong-field ionization process is exemplified by the direct and by the high-order above-threshold detachment of negative fluorine ions both for corotating and counterrotating bicircular fields. The symmetries of the electron distributions in the momentum plane are analyzed in detail. The results for laser-assisted electron-ion recombination and for high-order harmonic generation are presented for the bicircular field with counterrotating components.

Nondipole effects in strong-field ionization

We present a study of the relativistic nondipole effects in strong-field tunneling ionization process driven by a linearly polarized laser pulse. We consider the role of these effects in breaking the symmetry with respect to the inversion of the momentum component perpendicular to the laser-field polarization direction, which the dipole differential ionization probabilities possess. The study is based on the solution of a three-dimensional time-dependent Schr\odinger equation taking into account the leading-order relativistic corrections.

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.

Photon Energy Deposition in Strong-Field Single Ionization of Multielectron Molecules

Molecules exposed to strong laser fields may coherently absorb multiple photons and deposit the energy into electrons and nuclei, triggering the succeeding dynamics as the primary stage of the light-molecule interaction. We experimentally explore the electron-nuclear sharing of the absorbed photon energy in above-threshold multiphoton single ionization of multielectron molecules. Using CO as a prototype, vibrational and orbital resolved electron-nuclear sharing of the photon energy is observed. Different from the simplest one- or two-electron systems, the participation of the multiple orbitals and the coupling of various electronic states in the strong-field ionization and dissociation processes alter the photon energy deposition dynamics of the multielectron molecule. The population of numerous vibrational states of the molecular cation as the energy reservoir in the ionization process plays an important role in photon energy sharing between the emitted electron and the nuclear fragments.

Sub-barrier Coulomb effects on the interference pattern in tunneling-ionization photoelectron spectra

We use a quantum trajectory-based semi-classical method to account for Coulomb interaction between the photoelectron and the parent ion in the classically forbidden, sub-barrier region during strong-field tunneling ionization processes. We show that---besides the well-known modification of the tunneling ionization probability---there is also an influence on the interference pattern in the photoelectron spectra. In the long-wavelength limit, the shift of the intra-cycle interference fringes caused by sub-barrier Coulomb effects in the laser polarization direction can be derived analytically. We compare our results with \emph{ab initio} solutions of the time-dependent Schr\"odinger equation and find good agreement in the long-wavelength regime, whereas the standard strong field approximation fails. We show that the nodal structure along low-order above-threshold ionization rings is also affected by sub-barrier Coulomb effects.