Strong-field Tunneling Ionization Research Articles

Characterizing strong-field tunneling ionization with a phase-dependent THz polarization spectrum

The terahertz radiation emitted by asymmetrically ionized wavepackets in two-color strong-field tunneling ionization is essential for detecting the system's associated electron dynamics and structural properties. We propose to characterize and control tunneling ionization using a phase-dependent terahertz polarization (PTP) spectrum, analyzed through a combination of the classical trajectory Monte Carlo method, an analytical model based on the virial theorem, and the rigorous solution of the time-dependent Schrödinger equation as a benchmark. Our results demonstrate that the PTP spectrum offers a high-precision measure of the Coulomb effect through the relative phase of the two-color laser. Comparisons of PTP results calculated using different methods suggest how the electron can be manipulated by controlling the relative phase and laser intensity. In particular, the PTP spectrum can be used to calibrate the relative phase and provides a convenient and robust reconstruction of the time-averaging of tunneling positions with high precision using the analytical model. These insights reveal that the PTP spectrum as a whole can be a new and useful tool for the all-optical characterization of ultrafast atomic and molecular ionization.

Probing the electron motion in molecules using forward-scattering photoelectron holography.

Charge migration initiated by the coherent superposition of several electronic states is a basic process in intense laser-matter interactions. Observing this process on its intrinsic timescale is one of the central goals of attosecond science. Here, using forward-scattering photoelectron holography we theoretically demonstrate a scheme to probe the charge migration in molecules. In our scheme, by solving the time-dependent Schrödinger equation, the photoelectron momentum distributions (PEMDs) for strong-field tunneling ionization of the molecule are obtained. For a superposition state, it is shown that an intriguing shift of the holographic interference appears in the PEMDs, when the molecule is aligned perpendicularly to the linearly polarized laser field. With the quantum-orbit analysis, we demonstrate that this shift of the interference fringes is caused by the time evolution of the non-stationary superposition state. By analyzing the dependence of the shift on the final parallel momentum of the electrons, the relative phase and the expansion coefficient ratio of the two electronic states involved in the superposition state are determined accurately. Our study provides an efficient method for probing the charge migration in molecules. It will facilitate the application of the forward-scattering photoelectron holography to survey the electronic dynamics in more complex molecules.

The Surprising Dynamics of the McLafferty Rearrangement.

We report femtosecond time-resolved measurements of the McLafferty rearrangement following the strong-field tunnel ionization of 2-pentanone, 4-methyl-2-pentanone, and 4,4-dimethyl-2-pentanone. The pump-probe-dependent yields of the McLafferty product ion are fit to a biexponential function with fast (∼100 fs) and slow (∼10 ps) time constants, the latter of which is faster for the latter two compounds. Following nearly instantaneous ionization, the fast time scale is associated with rotation of the molecule to a six-membered cyclic intermediate that facilitates transfer of the γ-hydrogen, while the ∼50-100 times longer time scale is associated with a π-bond rearrangement and bond cleavage between the α- and β-carbons to produce the enol cation. These experimental measurements are supported by ab initio molecular dynamics trajectories, which further confirm the time scale of this important stepwise reaction in mass spectrometry.

Controlling Magnetic and Electric Nondipole Effects with Synthesized Two Perpendicularly Propagating Laser Fields

Nondipole effects are ubiquitous and crucial in light-matter interaction. However, they are too weak to be directly observed. In strong-field physics, motion of electrons is mainly confined in transverse plane of light fields, which suppresses the significance of nondipole effects. Here, we present a theoretical study on enhancing and controlling the nondipole effect by using the synthesized two perpendicularly propagating laser fields. We calculate the three-dimensional photoelectron momentum distributions of strong-field tunneling ionization of hydrogen atoms using the classical trajectory Monte Carlo model and show that the nondipole effects are noticeably enhanced in such laser fields due to their remarkable influences on the sub-cycle photoelectron dynamics. In particular, we reveal that the magnitudes of the magnetic and electric components of nondipole effects can be separately controlled by modulating the ellipticity and amplitude of driving laser fields. This novel scenario holds promising applications for future studies with ultrafast structured light fields.

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.

Subcycle-resolved strong-field tunneling ionization: Identification of magnetic dipole and electric quadrupole effects

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. Linear momentum transfer is a unique signature of the laser-atom interaction beyond its dipolar limit. Here, we present a decomposition of the subcycle time-resolved linear momentum transfer in term of its multipolar components. We show that the magnetic dipole contribution dominates the linear momentum transfer during the dynamical tunneling process while the post-ionization longitudinal momentum transfer in the field-driven motion of the electron in the continuum is primarily governed by the electric quadrupole interaction. Alternatively, exploiting the radiation gauge, we identify nondipole momentum transfer effects that scale either linearly or quadratically with the coupling to the laser field. The present results provide detailed insights into the physical mechanisms underlying the subcycle linear momentum transfer induced by nondipole effects.

Features of the molecular orbital in the photoelectron momentum distribution using elliptically polarized laser fields

We study the photoelectron momentum distribution from strong-field tunneling ionization of two molecules with similar highest occupied molecular orbitals, i.e., ${\mathrm{O}}_{2}$ and ${\mathrm{CO}}_{2}$. We find that the tiny difference between those two molecular orbitals can be clearly identified from the photoelectron momentum distributions in an elliptically polarized laser field, while it can hardly be identified in a linearly polarized laser field due to the strong Coulomb focusing effect. Furthermore, we show that the momentum distribution in the elliptically polarized laser field can be used to reveal how the molecular orbital affects the ionization time distribution of the photoelectron.

Nondipole Coulomb sub-barrier ionization dynamics and photon momentum sharing

The nondipole under-the-barrier dynamics of the electron during strong-field tunneling ionization is investigated, examining the role of the Coulomb field of the atomic core. The common analysis in the strong-field approximation is consequently generalized to include the leading light-front nondipole Coulomb corrections and demonstrates the counterintuitive impact of the sub-barrier Coulomb field. Despite its attractive nature, the sub-barrier Coulomb field increases the photoelectron nondipole momentum shift along the laser propagation direction, involving a strong dependence on the laser field. The scaling of the effect with respect to the principal quantum number and angular momentum of the bound state is found. We demonstrate that the signature of Coulomb induced sub-barrier effects can be identified in the asymptotic photoelectron momentum distribution via a comparative study of the field-dependent longitudinal momentum shift for different atomic species with state-of-the-art experimental techniques of midinfrared lasers.

Analyzing the electron trajectories in strong-field tunneling ionization with the phase-of-the-phase spectroscopy.

By numerically solving the time-dependent Schrödinger equation, we theoretically study strong-field tunneling ionization of Ar atom in the parallel two-color field which consists of a strong fundamental pulse and a much weaker second harmonic component. Based on the quantum orbits concept, we analyzed the photoelectron momentum distributions with the phase-of-the-phase spectroscopy, and the relative contributions of the two parts of the photoelectrons produced during the rising and falling edges of the adjacent quarters of the laser cycle are identified successfully. Our results show that the relative contributions of these two parts depend on both of the transverse and longitude momenta. By comparing the results from model atoms with Coulomb potential and short-range potential, the role of the long-range Coulomb interaction on the relative contributions of these two parts of electrons is revealed. Additionally, we show that the effects of Coulomb interaction on ionization time are vital for identifying their relative contributions.

Photoelectron holography in strong-field tunneling ionization by a spatially inhomogeneous field

Photoelectron holography in strong-field tunneling ionization is an efficient way to probe the structures and the ultrafast dynamics information of atoms and molecules. Manipulating the process of photoelectron holography is important for its application. Here, we study theoretically strong-field photoelectron holography in the spatially inhomogeneous field by solving the time-dependent Schr\"odinger equation. Our results show that the returning energy of the rescattering electron is greatly enhanced in the spatially inhomogeneous field, and the holographic interference pattern can be separated from other types of interference in the photoelectron momentum distribution. Moreover, our results show that the time window of tunneling ionization wherein the electron could be driven back to induce holography is broadened in the inhomogeneous field. These properties are beneficial for the application of photoelectron holography in probing the atomic and molecular structures and dynamics. The origin for these properties is analyzed with the classical trajectory model.

Attosecond-resolved photoelectron holography for triatomic molecule

Photoelectron holography in strong field tunneling ionization has subatomic spatial and attosecond temporal resolutions and thus it is a promising method to probe the attosecond electronic dynamics in atoms and molecules. The proof-of-concept studies have been performed in atoms and diatomic molecules. Here, we illustrate the application of the strong-field photoelectron holography in probing the attosecond electron dynamics in more complex system. As a demonstrated, by solving the time-dependent Schrödinger equation, we shown that the ultrafast charge migration in the triatomic molecule H3 could be retrieved from the holographic fringes in the photoelectron momentum distribution. Our study indicates that the concept of photoelectron holography can be extended to probe the attosecond electron dynamics in more complex molecules which is of essential significance for the newly emerging attosecond chemistry.

Dissecting subcycle interference in photoelectron holography

Multipath holographic interference in strong-field quantum tunnel ionization is key to revealing sub-Angstrom attosecond dynamics for molecular movies. This critical sub-cycle motion is often obscured by longer time-scale effects such as ring-shaped patterns that appear in above-threshold ionization (ATI). In the present work, we overcome this problem by combining two novel techniques in theory and experimental analysis: unit-cell averaging and time-filtering data and simulations. Together these suppress ATI rings and enable an unprecedented highly-detailed quantitative match between strong-field ionization experiments in argon and the Coulomb-quantum orbit strong-field approximation (CQSFA) theory. Velocity map images reveal fine modulations on the holographic spider-like interference fringes that form near the polarization axis. CQSFA theory traces this to the interference of three types of electron pathways. The level of agreement between experiment and theory allows sensitive determination of quantum phase differences and symmetries, providing an important tool for quantitative dynamical imaging in quantum systems.

Local most-probable routes and classical-quantum correspondence in strong-field two-dimensional tunneling ionization

We study ionization of atoms in strong two-dimensional (2D) laser fields with various forms, numerically and analytically. We focus on the local most-probable tunneling routes (some specific electron trajectories) which are corresponding to the local maxima of photoelectron momentum distributions (PMDs). By making classic-quantum correspondence, we obtain a condition for these routes characterized by the electron position at the tunnel exit. With comparing the identified routes with the classical limit and the partial-decoupling approximation where it is assumed that tunneling is dominated by the main component of the 2D field, some semiclassical properties of 2D tunneling are addressed. The local maxima of PMD related to the local most-probable routes can be used as one of the preferred observables in ultrafast measurements.

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.

Taking snapshots of a moving electron wave packet in molecules using photoelectron holography in strong-field tunneling ionization* *Project supported by the National Natural Science Foundation of China (Grant Nos. 11874163, 11604108, and 11604388), the Program for HUST Academic Frontier Youth Team, and the Fundamental Research Funds for the Central Universities, China (HUST No. 2017KFXKJC002).

Coherent superposition of electronic states induces attosecond electron motion in molecules. We theoretically investigate the strong-field ionization of this superposition state by numerically solving the time-dependent Schrödinger equation. In the obtained photoelectron momentum distribution, an intriguing bifurcation structure appears in the strong-field holographic interference pattern. We demonstrate that this bifurcation structure directly provides complete information about the status of the transient wave function of the superposition state: the horizontal location of the bifurcation in the momentum distribution reveals the relative phase of the involved components of the superposition state and the vertical position indicates the relative coefficient. Thus, this bifurcation structure takes a snapshot of the transient electron wave packet of the superposition state and provides an intuitive way to monitor electron motion in molecules.

Numerical and laboratory attoclock simulations on noble-gas atoms

We conduct a systematic theoretical study of strong field tunneling ionization of noble-gas atoms, from He to Kr, by elliptically polarized laser pulses in the so-called attoclock setup. Our theoretical model is based on a numerical solution of the time-dependent Schr\"odinger equation in the single active electron approximation. We simulate laboratory measurements utilizing few optical cycle pulses to benchmark our calculations against experiment. We further conduct ``numerical attoclock'' simulations with short, nearly single-cycle pulses to test various tunneling ionization models. We examine the attoclock offset angles as affected by the target orbital structure and the laser pulse intensity. Finally, we exclude a finite tunneling time scenario and attribute the attoclock offset angle entirely to the Coulomb field of the ion remainder as was recently demonstrated for the hydrogen atom [U. S. Sainadh et al., Nature (London) 568, 75 (2019)].

Ionization induced dynamic alignment of water

Two-body dissociation resulting from strong-field double ionization of water is investigated. Two distinct features are seen in the alignment of the fragment momenta with respect to the laser polarization. One feature shows alignment of the H-OH axis with the laser polarization, while the other indicates polarization alignment normal to the H-OH axis. By analyzing kinematic differences between the OH+/D+ and OD+/H+ channels of HOD, these two alignment features are shown to result from dissociation from different states in the dication. Only dissociation from one of these states has an alignment dependence consistent with predictions of sequential strong-field tunneling ionization models. The alignment dependence of dissociation from the other state can only be explained by dynamic alignment launched by the unbending of the molecule during ionization.

Resolving strong-field tunneling ionization with a temporal double-slit interferometer

Laser-induced tunneling ionization is one of the most fundamental and ubiquitous quantum processes and it initiates various ultrafast phenomena in intense laser-atom and laser-molecule interactions. Accurately resolving tunneling ionization is essential for understanding these phenomena. Based on the advanced attosecond technologies, such as high-order harmonic spectroscopy and strong-field photoelectron holography, previous studies have resolved the temporal properties of the tunneling process for rescattering electron. Here, as a complement, we theoretically demonstrate the retrieval of the time information of the tunneling process for the direct electron with the temporal double-slit interferometer. In this scheme, a weak second harmonic parallel to the fundamental field is added. By solving the time-dependent Schr\odinger equation, the photoelectron momentum distribution (PEMD) from strong-field tunneling ionization is obtained. Varying the relative phase of the parallel two-color field, the path of the ionized electrons periodically changes, leading to a shift of the time double-slit interference fringes in PEMDs. By analyzing the response of the interference fringes to the perturbation, the time information of direct electron in strong-field tunneling ionization is reconstructed. Interestingly, our results present excellent agreement with the complex time obtained from the quantum-orbit model.

Two-dimensional photoelectron holography in strong-field tunneling ionization by counter rotating two-color circularly polarized laser pulses.

Strong-field photoelectron holography (SFPH), originating from the interference of the direct electron and the rescattering electron in tunneling ionization, is a significant tool for probing structure and electronic dynamics in molecules. We theoretically study SFPH by counter rotating two-color circularly (CRTC) polarized laser pulses. Different from the case of the linearly polarized laser field, where the holographic structure in the photoelectron momentum distribution (PEMD) is clustered around the laser polarization direction, in the CRTC laser fields, the tunneling ionized electrons could recollide with the parent ion from different angles and thus the photoelectron hologram appears in the whole plane of laser polarization. This property enables structural information delivered by the electrons scattering the molecule from different angles to be recorded in the two-dimensional photoelectron hologram. Moreover, the electrons tunneling at different laser cycles are streaked to different angles in the two-dimensional polarization plane. This property enables us to probe the sub-cycle electronic dynamics in molecules over a long time window with the multiple-cycle CRTC laser pulses.

Unifying Tunneling Pictures of Strong-Field Ionization with an Improved Attoclock.

We demonstrate a novel attoclock, in which we add a perturbative linearly polarized light field at 400nm to calibrate the attoclock constructed by an intense circularly polarized field at 800nm. This approach can be directly implemented to analyze the recent hot and controversial topics involving strong-field tunneling ionization. The generally accepted picture is that tunneling ionization is instantaneous and that the tunneling probability synchronizes with the laser electric field. Alternatively, recently it was described in the Wigner picture that tunneling ionization would occur with a certain of time delay. We unify the two seemingly opposite viewpoints within one theoretical framework, i.e., the strong-field approximation (SFA). We illustrate that both the instantaneous tunneling picture and the Wigner time delay picture that are derived from the SFA can interpret the measurement well. Our results show that the finite tunneling delay will accompany nonzero exit longitudinal momenta. This is not the case for the instantaneous tunneling picture, where the most probable exit longitudinal momentum would be zero.