Tunneling Ionization Of Atoms Research Articles

Nonadiabatic tunneling ionization of atoms in few-cycle elliptically polarized laser pulses

We theoretically investigate nonadiabatic effects in tunneling ionization of a hydrogen atom induced by a few-cycle elliptically polarized laser pulse. We find a deflection angle between the maximum of the photoelectron momentum distribution and the direction of the negative vector potential corresponding to the electric-field peak. This deflection angle mainly originates from the fact that the instant of the maximal ionization rate does not exactly correspond to the instant of the electric-field peak in the few-cycle elliptically polarized laser pulse, revealing an ionization time shift between those two instants. The ionization time shift is a result of the nonadiabatic effect induced by the envelope of the few-cycle elliptically polarized laser pulse, which disappears in a long-pulsed laser. Our study is useful for understanding attoclock experiments using few-cycle elliptically polarized laser pulses.

Advances in response time of strong-field ionization of atoms

The response time of the electron to light in photoemission is difficult to define and measure. The tunneling ionization of atoms and molecules in a strong laser field is a type of strong field-induced photoelectric effect. In this process, the electron response time will change the time of high-order harmonic generation (HHG), which will have a fundamental influence on the reconstruction of electron attosecond dynamics through HHG. We propose a simple theory to resolve the response time problem in strong field atomic tunneling ionization. The response time corresponds to the strong interaction time of three bodies i.e. Coulomb, electron and laser field, which can be determined at the quantum-classical boundary. The observable directly obtained through response time can quantitatively reproduce a series of attoclock experimental curves and provide consistent explanations for these experimental phenomena. This work introduces the main conclusions of response time theory and summarizes in detail the research progress of this theory. Firstly, this theory can be applied to the orthogonal two-color laser field to quantitatively explain the main characteristic structures of photoelectron momentum distribution (PMD). Besides, with this response time theory, the scaling law of the observable in attoclock experiment can be obtained. The proposal of scaling law is expected to provide a systematical theoretical guide for better understanding the applicability or feasibility of the attoclock under different conditions. In addition, based on the atomic response time theory, we further consider the property of multi-center Coulomb potential of molecular and develop a response time theory suitable for molecular system. Subsequently, we further apply the response time theory to polar molecules, by utilizing the asymmetry of PMD closely related to response time to recognize the permanent dipole (PD) effect within the laser sub-cycle. In the end, we discuss the prospects for research on response time. Firstly, it is envisioned to further apply response time theory to weak light and single photon transition to detect the response time of related processes. Besides, considering the significant influence of response time on the property of time-domain of HHG electron trajectories, the recombination (re-scattering) effect based on the current strong field tunneling ionization response time theory can be further investigated, thus extending this theory to describing HHG and above threshold ionization (ATI) processes. Furthermore, designing the “re-scattering electron trajectories” reconstruction scheme based on the electron trajectories with response time correction will provide important suggestions for HHG spectroscopic experiments. Finally, considering the asymmetric ionization caused by the PD effect of polar molecules, if the net ionization yield of adjacent sub-cycles is used as the current indicator, polar molecules can be used as a “micro diode” to study a type of attosecond response switching device. Polar molecular diodes emit electrons through tunneling ionization in laser field. According to the response time theory, tunneling occurs almost instantaneously, and response time needs considering only at the tunneling exit. Based on this, by searching for suitable materials (such as two-dimensional materials), it is possible to design a type of semi-classical diode (which can utilize tunneling) with femtosecond or even sub-femtosecond response time. The response time theory can provide a convenient theoretical tool for designing of such tunneling diodes.

Non-exponential tunneling ionization probability distribution as a function of different laser beam profiles

In this paper, we discussed the probability distribution of exponential and non-exponential tunneling ionization of atoms, taking into account that the tunneling is not instantaneous, but requires a very short time interval. Also, it was investigated how different laser beam profiles affect the probability distribution. These physical situations are analyzed for the valence electron of potassium atom exposed to a strong laser field in a wide range of intensities (1012 -1015 W/cm2). We use ADK theory formalism to compute probability distributions. The results demonstrate that the probability distribution in the non-exponential mode has a significantly lower value than in the exponential mode, calculated under the same conditions. We showed that various laser beam profiles on these probability distributions produce different tunneling time intervals.

Initial longitudinal velocity resolved spiderlike photoelectron momentum distributions in hydrogen

Tunneling ionization of atoms is the basis of many phenomena and techniques, which requires people to be able to comprehensively understand this crucial physical process. Recent experiments have demonstrated the existence of the nonzero initial longitudinal momentum spread at the tunnel exit. However, the initial longitudinal velocity is usually set to be zero in the adiabatic regime. In this work, we numerically study that the initial longitudinal velocity of ionized-out electrons plays the role in the spiderlike photoelectron momentum distributions in hydrogen atom by using the semiclassical rescattering model and the time-dependent Schrödinger equation. Nonzero longitudinal initial velocity, no matter whether it is an offset or an offset distribution, is considered in the semiclassical rescattering model. Longitudinal cut-plot and transverse cut-plot of the photoelectron momentum distribution are discussed. The final longitudinal momentum of the electron is found to be sensitive to the initial longitudinal velocity, which offers us a method of determining the information about the initial longitudinal velocity from a photoelectron momentum distribution according to this linear relationship. We unveil that either an offset or an offset distribution for the initial longitudinal velocity can perfectly reproduce the same spiderlike photoelectron momentum distributions. The semiclassical results are backed by the full quantum simulation. It is expected that more precise research is required to deepen the knowledge of the initial longitudinal velocity in strong field ionization of atoms.

Tunneling delay time in strong field ionization of atomic Ar

“Attoclock” provides a promising experimental scheme to explore the timing of tunnel ionization of atoms and molecules in intense laser fields. In this work, we perform a systematical investigation of tunneling delay time in strong field ionization of atomic Ar, based on the “attoclock” experimental scheme. Experimentally, the laser intensity dependence of the photoelectron momentum distributions of Ar subject to strong elliptically polarized laser fields at 800 nm has been measured. Theoretically, a dedicated semiclassical model, in which the Coulomb potential effect, the nonadiabatic effect, the Stark effect, the multielectron screening and polarization effect have been well considered, is employed to simulate the ionization dynamics of Ar. By comparing the experimental and simulated results, an upper limit of 10 attoseconds for the tunneling delay time of Ar has been derived for the laser intensity ranges explored in this work. In addition, the influence of various physical effects on the extracted tunneling delay time, in the context of semiclassical model, has been analyzed. It is demonstrated that, under otherwise identical conditions, consideration of multielectron screening effect will give rise to the least change of the extracted tunneling delay time. In contrast, consideration of nonadiabatic effect will lead to the most significant change of the extracted tunneling delay time.

Resolving and weighing the quantum orbits in strong-field tunneling ionization

Tunneling ionization of atoms and molecules induced by intense laser pulses contains the contributions of numerous quantum orbits. Identifying the contributions of these orbits is crucial for exploring the application of tunneling and for understanding various tunneling-triggered strong-field phenomena. We perform a combined experimental and theoretical study to identify the relative contributions of the quantum orbits corresponding to the electrons tunneling ionized during the adjacent rising and falling quarter cycles of the electric field of the laser pulse. In our scheme, a perturbative second-harmonic field is added to the fundamental driving field. By analyzing the relative phase dependence of the signal in the photoelectron momentum distribution, the relative contributions of these two orbits are unambiguously determined. Our results show that their relative contributions sensitively depend on the longitudinal momentum and modulate with the transverse momentum of the photoelectron, which is attributed to the interference of the electron wave packets of the long orbit. The relative contributions of these orbits resolved here are important for the application of strong-field tunneling ionization as a photoelectron spectroscopy for attosecond time-resolved measurements.

Diagnostics of ultra-intense laser pulses using tunneling ionization

We revisit a recently proposed scheme (Ciappina et al 2019 Phys. Rev. A 99 043405) for accurate measurement of electromagnetic radiation intensities in a focus of high-power laser beams. The method is based on the observation of multiple sequential tunneling ionization of atoms and suggests determination of the peak intensity value from the appearance in the focal area ions with a certain charge number. Here we study the sensitivity of the approach to two essential factors: the focal volume effect and the tunneling ionization model chosen to calculate ionization rates. We show, on the one hand, that the results appear almost model independent for ionization of helium- and hydrogen-like ions and, on the other hand, that the focal averaging leaves the intensity-dependent features visible. Our findings are in favor to a practical implementation of the atomic diagnostics of extreme laser intensities.

Mutual Enhancement of Brunel Harmonics

A mechanism of a significant increase in the yield of Brunel harmonics, which are the lowest odd harmonics generated in a plasma in the process of tunnel ionization of atoms and molecules by an intense laser pulse, has been proposed and analyzed. This mechanism is based on the mutual enhancement of harmonics at the parametric interaction with the field at the fundamental frequency caused by the degenerate ionization-induced multiwave mixing. The results of analytical and numerical calculations show that this can increase the intensities of the generated harmonics by several orders of magnitude.

Understanding Tunneling Ionization of Atoms in Laser Fields using the Principle of Multiphoton Absorption**Supported by the National Natural Science Foundation of China under Grant Nos 11725417 and 11575027, the Joint Fund of the National Natural Science Foundation of China and the China Academy of Engineering Physics under Grant No U1730449, and the Science Challenge Project under Grant No TZ2018005.

The elaborate energy and momentum spectra of ionized electrons from atoms in laser fields suggest that the ionization dynamics described by tunneling theory should be modified. Although great efforts have been carried out within semiclassical models, there are few discussions describing the multiphoton absorption process within a quantum framework. Comparing the results obtained with the time-dependent Schrödinger equation (TDSE) and the Keldysh–Faisal–Reiss (KFR) theory, we study the nonperturbative effects of ionization dynamics beyond the KFR theory. The difference in momentum spectra between multiphoton and tunneling regimes is understood in a unified picture with virtual multiphoton absorption processes. For the multiphoton regime, the momentum spectra can be obtained by coherent interference of each periodic contribution. However, the interference of multiphoton absorption peaks will result in a complex structure of virtual multiphoton bands in the tunneling regime. It is shown that the virtual spectra will be almost continuous in the tunneling regime instead of the discrete levels found in the multiphoton regime. Finally, with a model combining the TDSE and the KFR theory, we try to understand the different effects of virtual multiphoton processes on ionization dynamics.

The Contribution of the Atomic Excitation and Recollision Effect during Tunneling Ionization on the Transition Rate

We used the Dykhne formalism to develop an analytical model for correlated simultaneous ionization excitation process of two-electron helium-like atoms in a strong laser field, and then analyzed the contribution of recollision effect on transition rate in a linearly polarized laser field. Also, we briefly discussed recollision effect in a circularly and linearly polarized laser field. We were interested to examine how atomic excitation and recollision affect the transition rate because observations indicated the significance of both processes on the tunneling ionization of atoms in a linearly polarized laser radiation. We showed that, under the conditions considered here, the aforementioned effects play an important role and, therefore, must be taken into account in the case of a linear polarization, while the recollision effect do not affect the rate in a circular polarization.

Tunneling ionization of atoms and ions in a linear electromagnetic wave and a constant magnetic field and the “imaginary time” method

The tunneling ionization of atoms and negative ions in an intense linearly polarized laser field and a constant uniform magnetic field is discussed in the quasiclassical theory framework. We use the “imaginary time” method, where tunneling is described by the classical equations of motion but with purely imaginary “time” to derive the extremal subbarrier trajectory of the photoelectron. This allows to obtain simple analytical expressions for ionization rates in the tunneling regime for an arbitrary angle between a laser beam and a constant magnetic field accounting for the Coulomb interaction of the photoelectron with the atomic core. The resonance case, when the frequency of a monochromatic electromagnetic wave and the cyclotron frequency are equal, is also considered. The limits of weak and strong magnetic fields and the expressions for the barrier width and the emission angle of photoelectrons are discussed. It is shown that a magnetic field in the presence of a linear electromagnetic wave increases the barrier width and thus decreases the ionization probability, i.e., stabilizes the bound level.

High-Frequency Quasi-Potential Waves in the Plasma Formed under Tunnel Ionization of Atoms

The dispersion law and collisionless damping rate of quasi-potential waves in the plasma formed upon tunnel ionization of gas atoms in the field of a short pulse of circularly or linearly polarized radiation are found. It is shown how the frequency and damping rate of quasi-potential waves depend on the wave propagation direction relative to the symmetry axis of the photoelectron distribution. It is established that, in plasma with a toroidal photoelectron velocity distribution, weakly damped waves with a linear dispersion law and frequency above the electron plasma frequency can propagate in a wide range of angles. In the case of a bi-Maxwellian photoelectron distribution, the frequency of weakly damped waves is comparable with the electron plasma frequency and the anisotropy of electron motion manifests itself in relatively small corrections to the dispersion law.

Tunnel ionization of atoms and molecules: How accurate are the weak-field asymptotic formulas?

Weak-field asymptotic formulas for the tunnel ionization rate of atoms and molecules in strong laser fields are often used for the analysis of strong field recollision experiments. We investigate their accuracy and domain of validity for different model systems by confronting them to exact numerical results, obtained by solving the time dependent Schrödinger equation. We find that corrections that take the dc-Stark shift into account are a simple and efficient way to improve the formula. Furthermore, analyzing the different approximations used, we show that error compensation plays a crucial role in the fair agreement between exact and analytical results.

High harmonic generation at the tunneling ionization of atoms by intense laser radiation near the classical cut-off

The yield of spontaneous photons at the tunneling ionization of atoms by intense low-frequency laser radiation near the classical cut-off is estimated analytically by using the three-step model. The Bell-shaped dependence in the universal photon spectrum is explained qualitatively.

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.

Nonadiabatic effects in electronic and nuclear dynamics.

Due to their very nature, ultrafast phenomena are often accompanied by the occurrence of nonadiabatic effects. From a theoretical perspective, the treatment of nonadiabatic processes makes it necessary to go beyond the (quasi) static picture provided by the time-independent Schrödinger equation within the Born-Oppenheimer approximation and to find ways to tackle instead the full time-dependent electronic and nuclear quantum problem. In this review, we give an overview of different nonadiabatic processes that manifest themselves in electronic and nuclear dynamics ranging from the nonadiabatic phenomena taking place during tunnel ionization of atoms in strong laser fields to the radiationless relaxation through conical intersections and the nonadiabatic coupling of vibrational modes and discuss the computational approaches that have been developed to describe such phenomena. These methods range from the full solution of the combined nuclear-electronic quantum problem to a hierarchy of semiclassical approaches and even purely classical frameworks. The power of these simulation tools is illustrated by representative applications and the direct confrontation with experimental measurements performed in the National Centre of Competence for Molecular Ultrafast Science and Technology.

Effects of orbital and Coulomb potential in strong-field nonadiabatic tunneling ionization of atoms

We study the intensity-dependent photoelectron differential momentum distributions from tunneling ionization of Kr and Xe atoms in circularly polarized laser fields. We measure the width of photoelectron momentum distribution along the laser propagation direction in conjunction with the most probable momentum in the polarization plane. The predictions of the available tunneling models do not agree with the measurement. We further present a semiclassical model for strong-field tunneling ionization of atoms in circularly polarized laser fields, in which we include the effect of the initial orbitals with different magnetic quantum numbers. Using this model, we quantify the relative contributions of the initial orbitals with different magnetic quantum numbers to the photoelectron differential momentum distributions. We achieve good agreement with the measurement, which does not depend on calibration of the laser intensity. Both the atomic orbitals and the long-range Coulomb potential have significant effects on the quantitative description of strong-field tunneling ionization of atoms.

Electron modes of plasma generated at tunnel ionization of atoms by a circularly polarized radiation

The collective modes of photoionized plasmas are studied using the model description of electron velocity distribution formed at tunnel ionization of atoms by circularly polarized radiation. The dispersion laws of transverse and approximately longitudinal high-frequency waves propagating at an arbitrary angle to the anisotropy axis of photoelectron distribution are obtained. The dispersion law of potential surface waves is derived. It is shown that the frequency of these waves may be greater than plasma frequency. The aperiodic instability of photoionized plasmas is described.

Experimental verification of the nonadiabatic effect in strong-field ionization with elliptical polarization

We perform high-resolution measurement of ellipticity-resolved momentum distributions from tunneling ionization of atoms along the major and minor axes in strong elliptically polarized fields, respectively. With developing a subcycle nonadiabatic strong-field tunneling theory for arbitrary laser polarization, we show that the electron initial conditions for positions and momenta after the tunneling are nonadiabatically intertwined with the instantaneous laser field. We extract the transverse and longitudinal momentum distributions at the tunnel exit with respect to the field ellipticity. We calibrate the laser intensity with ab initio calculation by solving the time-dependent Schr\"odinger equation. The nonadiabatic effects are confirmed experimentally and theoretically. Disentangling the effect of the long-range Coulomb potential from the laser field, we have further demonstrated that the momentum-time structure of the tunneling wave packet in strong laser fields can be approximatively imaged when treating the Coulomb effect perturbatively.

High-frequency waves in plasma formed as a result of tunnel ionization of atoms by circularly polarized radiation

New dependencies of frequency and damping decrement of high-frequency longitudinal waves on the wave vector in photoionized plasma formed by tunnel ionization of atoms in the field of circularly polarized radiation are found. Weakly damped longitudinal waves with a frequency much higher than the electron Langmuir frequency are predicted.