Under-the-barrier dynamics in laser-induced relativistic tunneling

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

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

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.

Nondipole Time Delay and Double-Slit Interference in Tunneling Ionization

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

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

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

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

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

Electric Nondipole Effect in Strong-Field Ionization

Strong-field ionization of atoms by circularly polarized femtosecond laser pulses produces a donut-shaped electron momentum distribution. Within the dipole approximation this distribution is symmetric with respect to the polarization plane. The magnetic component of the light field is known to shift this distribution forward. Here, we show that this magnetic nondipole effect is not the only nondipole effect in strong-field ionization. We find that an electric nondipole effect arises that is due to the position dependence of the electric field and which can be understood in analogy to the Doppler effect. This electric nondipole effect manifests as an increase of the radius of the donut-shaped photoelectron momentum distribution for forward-directed momenta and as a decrease of this radius for backwards-directed electrons. We present experimental data showing this fingerprint of the electric nondipole effect and compare our findings with a classical model and quantum calculations.

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.

Dissecting Strong-Field Excitation Dynamics with Atomic-Momentum Spectroscopy

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

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

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

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

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

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.

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.

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."

Strong Field Theories beyond Dipole Approximations in Nonrelativistic Regimes

The exact nondipole Volkov solutions to the Schrödinger equation and Pauli equation are found, based on which a strong field theory beyond the dipole approximation is built for describing the nondipole effects in nonrelativistic laser driven electron dynamics. This theory is applied to investigate momentum partition laws for multiphoton and tunneling ionization and explicitly shows that the complex interplay of a laser field and Coulomb action may reverse the expected photoelectron momentum along the laser propagation direction. The magnetic-spin coupling does not bring observable effects on the photoelectron momentum distribution and can be neglected. Compared to the strong field approximation within the dipole approximation, this theory works in a much wider range of laser parameters and lays a solid foundation for describing nonrelativistic electron dynamics in both short wavelength and midinfrared regimes where nondipole effects are unavoidable.

Electron spin fluctuation in intense laser fields

Spin fluctuation dynamics of diatomic and monoatomic ions interacting with ultrashort intense laser pulses is studied by solving the time-dependent Dirac equation.

Ionization Time and Exit Momentum in Strong-Field Tunnel Ionization

Tunnel ionization belongs to the fundamental processes of atomic physics. The so-called two-step model, which describes the ionization as instantaneous tunneling at the electric field maximum and classical motion afterwards with zero exit momentum, is commonly employed to describe tunnel ionization in adiabatic regimes. In this contribution, we show by solving numerically the time-dependent Schrödinger equation in one dimension and employing a virtual detector at the tunnel exit that there is a nonvanishing positive time delay between the electric field maximum and the instant of ionization. Moreover, we find a nonzero exit momentum in the direction of the electric field. To extract proper tunneling times from asymptotic momentum distributions of ionized electrons, it is essential to incorporate the electron's initial momentum in the direction of the external electric field.

Tunneling dynamics in multiphoton ionization and attoclock calibration

The intermediate domain of strong-field ionization between the tunneling and multiphoton regimes is investigated using the strong-field approximation and the imaginary-time method. An intuitive model for the dynamics is developed which describes the ionization process within a nonadiabatic tunneling picture with a coordinate dependent electron energy during the under-the-barrier motion. The nonadiabatic effects in the elliptically polarized laser field induce a transversal momentum shift of the tunneled electron wave packet at the tunnel exit and a delayed appearance in the continuum as well as a shift of the tunneling exit towards the ionic core. The latter significantly modifies the Coulomb focusing during the electron excursion in the laser field after exiting the ionization tunnel. We show that nonadiabatic effects are especially large when the Coulomb field of the ionic core is taken into account during the under-the-barrier motion. The simple man model modified with these nonadiabatic corrections provides an intuitive background for exact theories and has direct implications for the calibration of the attoclock technique.

Photon momentum sharing between an electron and an ion in photoionization: from one-photon (photoelectric effect) to multiphoton absorption

We investigate photon-momentum sharing between an electron and an ion following different photoionization regimes. We find very different partitioning of the photon momentum in one-photon ionization (the photoelectric effect) as compared to multiphoton processes. In the photoelectric effect, the electron acquires a momentum that is much greater than the single photon momentum ℏω/c [up to (8/5) ℏω/c] whereas in the strong-field ionization regime, the photoelectron only acquires the momentum corresponding to the photons absorbed above the field-free ionization threshold plus a momentum corresponding to a fraction (3/10) of the ionization potential Ip. In both cases, due to the smallness of the electron-ion mass ratio, the ion takes nearly the entire momentum of all absorbed N photons (via the electron-ion center of mass). Additionally, the ion takes, as a recoil, the photoelectron momentum resulting from mutual electron-ion interaction in the electromagnetic field. Consequently, the momentum partitioning of the photofragments is very different in both regimes. This suggests that there is a rich, unexplored physics to be studied between these two limits which can be generated with current ultrafast laser technology.

Breakdown of the dipole approximation in strong-field ionization

We report the breakdown of the electric dipole approximation in the long-wavelength limit in strong-field ionization with linearly polarized few-cycle mid-infrared laser pulses at intensities on the order of 10¹³ W/cm². Photoelectron momentum distributions were recorded by velocity map imaging and projected onto the beam propagation axis. We observe an increasing shift of the peak of this projection opposite to the beam propagation direction with increasing laser intensities. From a comparison with semiclassical simulations, we identify the combined action of the magnetic field of the laser pulse and the Coulomb potential as the origin of our observations.