Tunneling Ionization Time Resolved by Backpropagation

Photocurrent-induced harmonics in nanostructures

Photocurrent-induced harmonics appear in gases and solids due to tunnel ionization of electrons in strong fields and subsequent acceleration. In contrast to three-step harmonic emission, no return to the parent ions is necessary. Here we show that the same mechanism produces harmonics in metallic nanostructures in strong fields. Furthermore, we demonstrate how strong local field gradient, appearing as a consequence of the field enhancement, affects photocurrent-induced harmonics. This influence can shed light at the state of electron as it appears in the continuum, in particular, to its initial velocity.

Observation of Attosecond Time Delays in Above-Threshold Ionization

Attosecond-scale temporal characterization of photoionization is essential in understanding how light and matter interact on the most fundamental level. However, characterizing the temporal property of strong-field above-threshold ionization has remained unreached. Here, we propose a novel photoelectron interferometric method to disentangle the contribution of Coulomb effect from an attoclock, allowing us to clock energy-resolved time delays of strong-field above-threshold ionization. We disentangle two types of Coulomb effects for the attoclock, i.e., one arising from the Coulomb disturbance of a single electron trajectory and the second effect arising from the photoelectron phase space distortion due to the Coulomb field. We find that the second Coulomb effect manifests itself as an energy-resolved attosecond time delay in the electron emission, which is relevant to the effect of nonadiabatic initial longitudinal momentum at the tunnel exit. Our study further indicates a sensitivity of the time delay to the temporal profile of the released electron wave packet within one half laser cycle. The temporal width of the released electron wave packet is found to increase with energy, which contradicts the common assumption in the adiabatic picture.

Strong-Field Ionization Phenomena Revealed by Quantum Trajectories

We investigate the photoionization dynamics of atoms subjected to intense, ultrashort laser pulses through the use of quantum trajectories. This method provides a unique and consistent framework for examining electron dynamics within a time-dependent potential barrier. Our findings demonstrate that quantum trajectories offer additional insights into several key aspects of strong-field ionization, including the transition between ionization regimes, nonadiabatic effects under the barrier, the impact of the shape of the electronic potential, and the efficiency of over-the-barrier ionization.

Probing and Steering Attosecond Electron Motion Using Tailored Ultrafast Laser Fields

An ultrafast intense laser field is one of the most important tools to observe and manipulate electronic and nuclear dynamics with subcycle precision in highly nonlinear light-matter interactions, which provides access to attosecond chemistry and physics. In this review, we briefly summarize the protocol of attosecond chronoscopy and its application in probing the attosecond photoemission dynamics from atoms and molecules. We also review the control schemes of attosecond electron motion in atoms and molecules as well as molecular bond formation and cleavage with the assistance of tailored femtosecond laser fields.

Tunnelling of electrons via the neighboring atom

As compared to the intuitive process that the electron emits straight to the continuum from its parent ion, there is an alternative route that the electron may transfer to and be trapped by a neighboring ionic core before the eventual release. Here, we demonstrate that electron tunnelling via the neighboring atomic core is a pronounced process in light-induced tunnelling ionization of molecules by absorbing multiple near-infrared photons. We devised a site-resolved tunnelling experiment using an Ar-Kr+ ion as a prototype system to track the electron tunnelling dynamics from the Ar atom towards the neighboring Kr+ by monitoring its transverse momentum distribution, which is temporally captured into the resonant excited states of the Ar-Kr+ before its eventual releasing. The influence of the Coulomb potential of neighboring ionic cores promises new insights into the understanding and controlling of tunnelling dynamics in complex molecules or environment.

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.

Reconciling Conflicting Approaches for the Tunneling Time Delay in Strong Field Ionization

Several recent attoclock experiments have investigated the fundamental question of a quantum mechanically induced time delay in tunneling ionization via extremely precise photoelectron momentum spectroscopy. The interpretations of those attoclock experimental results were controversially discussed, because the entanglement of the laser and Coulomb field did not allow for theoretical treatments without undisputed approximations. The method of semiclassical propagation matched with the tunneled wave function, the quasistatic Wigner theory, the analytical R-matrix theory, the backpropagation method, and the under-the-barrier recollision theory are the leading conceptual approaches put forward to treat this problem, however, with seemingly conflicting conclusions on the existence of a tunneling time delay. To resolve the contradicting conclusions of the different approaches, we consider a very simple tunneling scenario which is not plagued with complications stemming from the Coulomb potential of the atomic core, avoids consequent controversial approximations and, therefore, allows us to unequivocally identify the origin of the tunneling time delay.

Probing Resonant Photoionization Time Delay by Self-Referenced Molecular Attoclock

Attosecond time-resolved electron tunneling dynamics have been investigated by using attosecond angular streaking spectroscopy, where a clock reference to the laser field vector is required in atomic strong-field ionization and the situation becomes complicated in molecules. Here we reveal a resonant ionization process via a transient state by developing an electron-tunneling-site-resolved molecular attoclock in Ar-Kr^{+}. Two distinct deflection angles are observed in the photoelectron angular distribution in the molecular frame, corresponding to the direct and resonant ionization pathways. We find the electron is temporally trapped in the Coulomb potential wells of the Ar-Kr^{+} before finally releasing into the continuum when the electron tunnels through the internal barrier. By utilizing the direct tunneling ionization as a self-referenced arm of the attoclock, the time delay of the electron trapped in the resonant state is revealed to be 3.50±0.04  fs. Our results give an impetus to exploring the ultrafast electron dynamics in complex systems and also endow a semiclassical presentation of the electron trapping dynamics in a quantum resonant state.

Full experimental determination of tunneling time with attosecond-scale streaking method

Tunneling is one of the most fundamental and ubiquitous processes in the quantum world. The question of how long a particle takes to tunnel through a potential barrier has sparked a long-standing debate since the early days of quantum mechanics. Here, we propose and demonstrate a novel scheme to accurately determine the tunneling time of an electron. In this scheme, a weak laser field is used to streak the tunneling current produced by a strong elliptically polarized laser field in an attoclock configuration, allowing us to retrieve the tunneling ionization time relative to the field maximum with a precision of a few attoseconds. This overcomes the difficulties in previous attoclock measurements wherein the Coulomb effect on the photoelectron momentum distribution has to be removed with theoretical models and it requires accurate information of the driving laser fields. We demonstrate that the tunneling time of an electron from an atom is close to zero within our experimental accuracy. Our study represents a straightforward approach toward attosecond time-resolved imaging of electron motion in atoms and molecules.

Nonadiabatic Strong Field Ionization of Atomic Hydrogen

We present experimental data on the nonadiabatic strong field ionization of atomic hydrogen using elliptically polarized femtosecond laser pulses at a central wavelength of 390 nm. Our measured results are in very good agreement with a numerical solution of the time-dependent Schrödinger equation (TDSE). Experiment and TDSE show four above-threshold ionization peaks in the electron's energy spectrum. The most probable emission angle (also known as "attoclock offset angle" or "streaking angle") is found to increase with energy, a trend that is opposite to standard predictions based on Coulomb interaction with the ion. We show that this increase of deflection angle can be explained by a model that includes nonadiabatic corrections of the initial momentum distribution at the tunnel exit and nonadiabatic corrections of the tunnel exit position itself.

Observation of the Decrease of Larmor Tunneling Times with Lower Incident Energy

How much time does a tunneling particle spend in a barrier? A Larmor clock, one proposal to answer this question, measures the interaction between the particle and the barrier region using an auxiliary degree of freedom of the particle to clock the dwell time inside the barrier. We report on precise Larmor time measurements of ultracold ^{87}Rb atoms tunneling through an optical barrier, which confirm longstanding predictions of tunneling times. We observe that atoms generally spend less time tunneling through higher barriers and that this time decreases for lower energy particles. For the lowest measured incident energy, at least 90% of transmitted atoms tunneled through the barrier, spending an average of 0.59±0.02  ms inside. This is 0.11±0.03  ms faster than atoms traversing the same barrier with energy close to the barrier's peak and 0.21±0.03  ms faster than when the atoms traverse a barrier with 23% less energy.

Dialogue on analytical and ab initio methods in attoscience

The perceived dichotomy between analytical and ab initio approaches to theory in attosecond science is often seen as a source of tension and misconceptions. This Topical Review compiles the discussions held during a round-table panel at the 'Quantum Battles in Attoscience' cecam virtual workshop, to explore the sources of tension and attempt to dispel them. We survey the main theoretical tools of attoscience-covering both analytical and numerical methods-and we examine common misconceptions, including the relationship between ab initio approaches and the broader numerical methods, as well as the role of numerical methods in 'analytical' techniques. We also evaluate the relative advantages and disadvantages of analytical as well as numerical and ab initio methods, together with their role in scientific discovery, told through the case studies of two representative attosecond processes: non-sequential double ionisation and resonant high-harmonic generation. We present the discussion in the form of a dialogue between two hypothetical theoreticians, a numericist and an analytician, who introduce and challenge the broader opinions expressed in the attoscience community.

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

Nonadiabatic effects in the double ionization of atoms driven by a circularly polarized laser pulse

We study the double ionization of atoms subjected to circularly polarized (CP) laser pulses. We analyze two fundamental ionization processes: the sequential (SDI) and nonsequential (NSDI) double ionization in the light of the rotating frame (RF) which naturally embeds nonadiabatic effects in CP pulses. We use and compare two adiabatic approximations: The adiabatic approximation in the laboratory frame (LF) and the adiabatic approximation in the RF. The adiabatic approximation in the RF encapsulates the energy variations of the electrons on subcycle timescales happening in the LF and this, by fully taking into account the ion-electron interaction. This allows us to identify two nonadiabatic effects including the lowering of the threshold intensity at which over-the-barrier ionization happens and the lowering of the ionization time of the electrons. As a consequence, these nonadiabatic effects facilitate over-the-barrier ionization and recollision-induced ionizations. We analyze the outcomes of these nonadiabatic effects on the recollision mechanism. We show that the laser envelope plays an instrumental role in a recollision channel in CP pulses at the heart of NSDI.

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.

The Photoionization Time in π-Conjugated Molecular Systems

The photoionization time of C₂H₄ is calculated as a model for π-conjugated molecular systems. Analytical results are obtained using the Wigner phase delay, which is compared with energy-streaking measurements. We find that, although the ionization time averaged over nuclear configurations compares well in the two measures, the dependence on the nuclear configuration is different. Interference between different ionization pathways depends significantly on the molecular geometry and the ionizing electron energy and may lead to qualitative changes in the ionization time.

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.

Attosecond Molecular Angular Streaking with All-Ionic Fragments Detection

Attosecond angular streaking (or "attoclock") is an insightful technique for probing the ultrafast electron dynamics in strong laser fields. Up until recently, this technique relied solely on an accurate measurement of the photoelectron momentum distribution and has remained restricted to atomic targets. Here, we propose a novel attosecond angular streaking scheme applicable to molecules, for which the ionic fragments of dissociative ionization are detected in the polarization plane of a close-to-circular polarized laser light. Our ionic attoclock measurements are consistent with theoretical results from a numerical solution of the time-dependent Schrödinger equation and an upper bound of 10 as on the tunneling time from the attoclock readings in the H_{2} molecule has been given, which is significantly smaller than any definitions of tunneling time available in the literatures.

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 400 nm to calibrate the attoclock constructed by an intense circularly polarized field at 800 nm. 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.

Photoelectron Holographic Interferometry to Probe the Longitudinal Momentum Offset at the Tunnel Exit

Laser-induced electron tunneling underlies numerous emerging spectroscopic techniques to probe attosecond electron dynamics in atoms and molecules. The improvement of those techniques requires an accurate knowledge of the exit momentum for the tunneling wave packet. Here we demonstrate a photoelectron interferometric scheme to probe the electron momentum longitudinal to the tunnel direction at the tunnel exit by measuring the photoelectron holographic pattern in an orthogonally polarized two-color laser pulse. In this scheme, we use a perturbative 400-nm laser field to modulate the photoelectron holographic fringes generated by a strong 800-nm pulse. The fringe shift offers direct experimental access to the intermediate canonical momentum of the rescattering electron, allowing us to reconstruct the momentum offset at the tunnel exit with high accuracy. Our result unambiguously proves the existence of nonzero initial longitudinal momentum at the tunnel exit and provides fundamental insights into the nonquasistatic nature of the strong-field tunneling.

Attosecond angular streaking and tunnelling time in atomic hydrogen

The tunnelling of a particle through a potential barrier is a key feature of quantum mechanics that goes to the core of wave-particle duality. The phenomenon has no counterpart in classical physics, and there are no well constructed dynamical observables that could be used to determine 'tunnelling times'. The resulting debate^1-5 about whether a tunnelling quantum particle spends a finite and measurable time under a potential barrier was reignited in recent years by the advent of ultrafast lasers and attosecond metrology⁶. Particularly important is the attosecond angular streaking ('attoclock') technique⁷, which can time the release of electrons in strong-field ionization with a precision of a few attoseconds. Initial measurements^7-10 confirmed the prevailing view that tunnelling is instantaneous, but later studies^11,12 involving multi-electron atoms-which cannot be accurately modelled, complicating interpretation of the ionization dynamics-claimed evidence for finite tunnelling times. By contrast, the simplicity of the hydrogen atom enables precise experimental measurements and calculations^13-15 and makes it a convenient benchmark. Here we report attoclock and momentum-space imaging¹⁶ experiments on atomic hydrogen and compare these results with accurate simulations based on the three-dimensional time-dependent Schrödinger equation and our experimental laser pulse parameters. We find excellent agreement between measured and simulated data, confirming the conclusions of an earlier theoretical study¹⁷ of the attoclock technique in atomic hydrogen that presented a compelling argument for instantaneous tunnelling. In addition, we identify the Coulomb potential as the sole cause of the measured angle between the directions of electron emission and peak electric field: this angle had been attributed^11,12 to finite tunnelling times. We put an upper limit of 1.8 attoseconds on any tunnelling delay, in agreement with recent theoretical findings¹⁸ and ruling out the interpretation of all commonly used 'tunnelling times'¹⁹ as 'time spent by an electron under the potential barrier'²⁰.

Identification of tunneling and multiphoton ionization in intermediate Keldysh parameter regime

Quantitative identification of tunneling ionization (TI) and multiphoton ionization (MPI) with Keldysh parameter γ in intermediate regime is of great importance to better understand various ionization-triggered strong-field phenomena. We theoretically demonstrate that the numerical observable ionization delay time is a more reliable indicator for characterizing the transition from TI to MPI under different laser parameters. Using non-linear iterative curve fitting algorithm (NICFA), the detected time-dependent probability current of ionized electrons can be decoupled into weighted TI and MPI portions. This enables us to confirm that the observed plateau-like structure in ionization delay time picture at the intermediate γ originates from the competition between TI and MPI processes. A hybrid quantum and classical approach (HQCA) is developed to evaluate the weights of TI and MPI electrons in good agreement with NICFA result. Moreover, the well separated TI and MPI electrons using HQCA are further propagated classically for mapping their final momentum, which well reproduces the experimental or ab-initio numerical calculated signatures of ionized electron momentum distribution in a rather broad γ regime.

Detecting and Characterizing the Nonadiabaticity of Laser-Induced Quantum Tunneling

The nonadiabaticity of quantum tunneling through an evolving barrier is relevant to resolving laser-driven dynamics of atoms and molecules at an attosecond timescale. Here, we propose and demonstrate a novel scheme to detect the nonadiabatic behavior of tunnel ionization studied in an attoclock configuration, without counting on the laser intensity calibration or the modeling of the Coulomb effect. In our scheme, the degree of nonadiabaticity for tunneling scenarios in elliptically polarized laser fields can be steered continuously simply with the pulse ellipticity, while the critical instantaneous vector potentials remain identical. We observe the characteristic feature of the measured photoelectron momentum distributions, which matches the distinctive prediction of nonadiabatic theories. In particular, our experiments demonstrate that the nonadiabatic initial transverse momentum at the tunnel exit is approximately proportional to the instantaneous effective Keldysh parameters in the tunneling regime, as predicted theoretically by Ohmi, Tolstikhin, and Morishita [Phys. Rev. A 92, 043402 (2015)PLRAAN1050-294710.1103/PhysRevA.92.043402]. Our study clarifies a long-standing controversy over the validation of the adiabatic approximation and will substantially advance studies of laser-induced ultrafast dynamics in experiments.

Deformation of Atomic p_{±} Orbitals in Strong Elliptically Polarized Laser Fields: Ionization Time Drifts and Spatial Photoelectron Separation

We theoretically investigate the deformation of atomic p_{±} orbitals driven by strong elliptically polarized (EP) laser fields and the role it plays in tunnel ionization. Our study reveals that different Stark effects induced by orthogonal components of the EP field give rise to subcycle rearrangement of the bound electron density, rendering the initial p_{+} and p_{-} orbitals deformed and polarized along distinctively tilted angles with respect to the polarization ellipse of the EP field. As a consequence, the instantaneous tunneling rates change such that for few-cycle EP laser pulses the bound electron initially counterrotating (corotating) with the electric field is most likely released before (after) the peak of the electric field. We demonstrate that with a sequential-pulse setup one can exploit this effect to spatially separate the photoelectrons detached from p_{+} and p_{-} orbitals, paving the way towards robust control of spin-resolved photoemission in laser-matter interactions.

Keldysh-Rutherford Model for the Attoclock

We demonstrate a clear similarity between attoclock offset angles and Rutherford scattering angles taking the Keldysh tunneling width as the impact parameter and the vector potential of the driving pulse as the asymptotic velocity. This simple model is tested against the solution of the time-dependent Schrödinger equation using hydrogenic and screened (Yukawa) potentials of equal binding energy. We observe a smooth transition from a hydrogenic to "hard-zero" intensity dependence of the offset angle with variation of the Yukawa screening parameter. Additionally, we make a comparison with the attoclock offset angles for various noble gases obtained with the classical-trajectory Monte Carlo method. In all cases we find a close correspondence between the model predictions and numerical calculations. This suggests a largely Coulombic origin of the attoclock offset angle and casts further doubt on its interpretation in terms of a finite tunneling time.

Under-the-Tunneling-Barrier Recollisions in Strong-Field Ionization

A new pathway of strong-laser-field-induced ionization of an atom is identified which is based on recollisions under the tunneling barrier. With an amended strong-field approximation, the interference of the direct and the under-the-barrier recolliding quantum orbits are shown to induce a measurable shift of the peak of the photoelectron momentum distribution. The scaling of the momentum shift is derived relating the momentum shift to the tunneling delay time according to the Wigner concept. This allows us to extend the Wigner concept for the quasistatic tunneling time delay into the nonadiabatic domain. The obtained corrections to photoelectron momentum distributions are also relevant for state-of-the-art accuracy of strong-field photoelectron spectrograms in general.

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.

Exploring tunneling time by instantaneous ionization rate in strong-field ionization

A quantum approach is presented to investigate tunneling time by supervising the instantaneous ionization rate. We find that the ionization rate peak appearance lags behind the maximum of electric field intensity for a linearly polarized pulse. This time delay interval can be taken to characterize the tunneling time. In addition, if an atom with anisotropic electronic distribution is exposed to a circular polarized pulse, the tunneling time can also be measured and defined as the time difference between the instant of the largest ionization rate and the moment when the electric field points in the maximum of the bound electron density.

Experimental Evidence for Quantum Tunneling Time

The first hundred attoseconds of the electron dynamics during strong field tunneling ionization are investigated. We quantify theoretically how the electron's classical trajectories in the continuum emerge from the tunneling process and test the results with those achieved in parallel from attoclock measurements. An especially high sensitivity on the tunneling barrier is accomplished here by comparing the momentum distributions of two atomic species of slightly deviating atomic potentials (argon and krypton) being ionized under absolutely identical conditions with near-infrared laser pulses (1300 nm). The agreement between experiment and theory provides clear evidence for a nonzero tunneling time delay and a nonvanishing longitudinal momentum of the electron at the "tunnel exit."

Numerical Detector Theory for the Longitudinal Momentum Distribution of the Electron in Strong Field Ionization

The lack of analytical solutions for the exit momentum in the laser-driven tunneling theory is a well-recognized problem in strong field physics. Theoretical studies of electron momentum distributions in the neighborhood of the tunneling exit depend heavily on ad hoc assumptions. In this Letter, we apply a new numerical method to study the exiting electron's longitudinal momentum distribution under intense short-pulse laser excitation. We present the first realizations of the dynamic behavior of an electron near the so-called tunneling exit region without adopting a tunneling approximation.