Radiation during strong-field tunneling ionization is investigated. The spontaneous as well as the coherent components of the radiation are calculated describing the ionization dynamics via the strong-field approximation, and the role of the quantum dynamics at tunneling is analyzed. The competition between different mechanisms in different spectral regions is examined. Transitionlike radiation (Brunel radiation) is dominant at low frequencies, Thomson scattering at the laser frequency, and radiative recombination via the three-step process at high-order harmonics. To distinguish the role of the quantum dynamics, simple man Drude models are developed for coherent as well as for spontaneous radiation; the models are based on the electron trajectory out of the tunneling barrier. The quantum dynamics is shown to modify the coherent Brunel radiation for near-zero frequencies in asymmetric laser pulses. The significant role of free-free transitions is demonstrated for spontaneous radiation in the low-frequency region.

Optical-field sampling using second-harmonic generation (SHG) from strong-field ionization enables ultrabroadband terahertz detection, but the microscopic origin of the SHG signal and its ultrabroadband response have been unclear. Here we show that the target field lifts the half-cycle cancellation of photoelectron dipole emission, generating the SHG signal used for field sampling. Time-dependent Schrodinger-equation simulations, supported by classical-trajectory Monte Carlo analysis, demonstrate that the SHG yield directly encodes the instantaneous target electric field at the ionization time, enabling waveform retrieval by scanning the probe-target delay. Because the SHG response is gated by a subcycle ionization window rather than the probe envelope, the detection bandwidth can extend far beyond the probe duration. We further quantify practical constraints on retrieval, including intrinsic probe asymmetry and SHG back-action, providing a predictive framework to optimize sensitivity, temporal resolution, and fidelity through controlled electron dynamics.

Previous attoclock experiments measuring the photoelectron momentum distribution (PMD) via strong-field ionization in an elliptically polarized laser field have shown anomalously large offset angles in the nonadiabatic regime with large Keldysh parameters (γ). We investigate the process theoretically in the complete range of ellipticity (ϵ) and large range of γ, employing numerical solutions of time-dependent Schrödinger equation and nonadiabatic classical-trajectory Monte Carlo simulations matched with the under-the-barrier motion via the nonadiabatic strong field approximation. We show the formation of low-energy structures (LES) at any ellipticity value when the Keldysh parameter is sufficiently large. Three regimes of the interaction in the (ϵ-γ)-space of parameters are identified via the characteristic PMD features. The significant modification of the recollision picture in the nonadiabatic regime, with so-called anomalous and hybrid slow recollisions, is shown to be behind the LES, inducing extreme nonlinear Coulomb bunching in the phase-space in the polarization plane. Our findings elucidate subtle features of the attosecond electron dynamics in strong-field ionization at extreme conditions and indicate limitations on attosecond imaging.

Ever since the advent of quantum mechanics, tunneling has been an intriguing topic and consequently extensively studied and utilized. Investigating both theoretically and experimentally the nonadiabatic tunneling in strong-field ionization across a wide range of laser intensities, we unravel under-the-barrierrecollision dynamics leading to Freeman resonances (FR). The under-the-barrier-recollision model, which goes beyond the traditional direct multiphoton transition description, predicts distinct features of FR phenomena that cannot be explained by the existing direct multiphoton transition scenario. Specifically, it predicts (i) the dominance of high-order FR over above-threshold ionization in the photoelectron energy spectra and (ii) the flat dependence of the FR signal on the laser intensity, both in the nonadiabatic tunneling regime. This Letter experimentally demonstrates these features, corroborating the under-thebarrier-recollision model, and provides intuition into this dynamics, expanding our insights into the control of tunneling dynamics in laser spectroscopy and attosecond physics.

Understanding of subtle features in the photoelectron momentum distribution (PMD) in strong-field ionization is vital for ultrafast imaging. One of such features, low-energy structures (LES) are typically linked to Coulomb effects in linearly polarized laser fields, leaving their formation in elliptically polarized fields unexplored. Here we demonstrate, employing numerical solutions of the time-dependent Schrödinger equation and nonadiabatic classical-trajectory Monte Carlo simulations, that the LES induced by specific recollisions persist at any laser ellipticity, provided the nonadiabatic regime is reached with sufficiently large nonadiabaticity. The significant modification of the recollision picture in the nonadiabatic regime, with so-called anomalous and hybrid slow recollisions, is shown to be behind the LES, inducing extreme nonlinear Coulomb bunching in the phase-space. Three regimes of the interaction are identified via the PMD characteristics. Our findings elucidate fine features of the attosecond electron dynamics in strong-field ionization at extreme conditions and indicate limitations on attosecond imaging. Low-energy structures (LES) in the photoelectron momentum distribution, typically observed in linearly polarized tunneling ionization, are caused by Coulomb effects. The authors demonstrate that the LES induced by specific recollisions persists at any laser ellipticity, provided the nonadiabatic regime is reached with sufficiently large nonadiabaticity.

A relativistic analytical theory of strong-field ionization applicable across the regimes of deep tunneling up to over-the-barrier ionization (OTBI) is developed, accounting also for the bound-state polarization and the Stark shift beyond perturbation theory. The latter improvement with respect to the state-of-the-art quasiclassical theory of Perelomov-Popov-Terent'ev (PPT) for strong-field ionization is essential to describe analytically the ionization in the OTBI regime and to resolve the order-of-magnitude discrepancy of the ionization yield in the relativistic regime with respect to PPT theory that has remained unexplained since the numerical result using the Klein-Gordon equation of Hafizi []. The predictions of the present relativistic model, in deviation to PPT theory, are shown to be observable using ultrashort laser pulses of relativistic intensities. Published by the American Physical Society 2024

A relativistic analytical theory of strong field ionization applicable across the regimes of the deep-tunneling up to the over-barrier ionization (OTBI) is developed, incorporating the effects of the polarization of the atomic bound state and the Stark-shift in an ultrastrong laser field. The theory, in particular, addresses the order of magnitude discrepancy of the ionization yield in the relativistic regime calculated via the numerical solution of the Klein-Gordon equation [B. Hafizi \textit{et al}., Phys. Rev. Lett. 118, 133201 (2017)] with respect to the state-of-the-art quasiclassical theory of Perelomov-Popov-Terent'ev (PPT) for strong field ionization. The developed theory employs a Keldysh-like approach describing the ionization as an adiabatic quantum jump from the bound state to the continuum at a specific transition time, where the improved performance is achieved by accounting for the bound state distortion in the laser field. In the nonrelativistic limit, our theory reproduces the well-known fit to the numerical calculations for the OTBI rate via the Tong-Lin factor. Realistic conditions for an experimental confirmation of the prediction of the present relativistic model versus PPT-theory are also presented.

The time delay in strong field tunneling ionization presents a captivating challenge in the field of attoscience. It is linked to the phase of the photoelectron wavepacket, a relationship that modern attosecond photoelectron interferometry can effectively probe. However, the connection between sub-barrier dynamics and the phase formation remains unclear. In this study, we investigate the role of under-the-barrier recollisions for shaping the phase of the photoelectron wavepacket. We establish a general analytical relationship between the phase of the tunneled electron wavepacket and the tunneling rate. Our results demonstrate that the Coulomb field effect of the atomic potential enhances both the amplitude of the recolliding path and the phase shift of the wavepacket, effectively countering the lateral spreading of the tunneling wavepacket during sub-barrier propagation. The insights gained from this research will aid in the development of free electron wavepackets with tailored properties through strong field ionization. This work investigates the origin of time delay in strong field tunneling ionization and its relation to the parameters of the photoelectron wavepacket. The authors establish a general analytical relationship between the phase of the wavepacket and the tunneling rate, and analyze the role of under-the-barrier recollisions for shaping the photoelectron wavepacket.

Tunneling ionization is characterized by a negative time delay, observed asymptotically as a specific shift of the photoelectron momentum distribution, which is caused by the interference of the sub-barrier recolliding and direct ionization paths. In contrast, a \textit{Gedankenexperiment} following the peak of the wavefunction shows a positive tunneling time delay at the tunnel exit, considering only the direct ionization path. In this paper, we investigate the effects of sub-barrier recollisions on the time delay pattern at the tunnel exit. We conclude that the interference of the direct and recolliding trajectories decreases the tunneling time delay at the exit by the value equal to the asymptotic time delay maintaining, however, its sizeable positive value. Finally, we discuss the recent experiment [Light: Science \& Applications 11, 1 (2022)] addressing the tunneling time in a modified two-color attoclock setup. The analysis of the experimental findings with our theoretical model indicates the physical necessity to introduce a new time characteristic for tunneling ionization -- the time delay describing the initiation of the tunneling wave packet.

Relativistic strong-field ionization of hydrogen-like atoms or ions in a constant crossed electromagnetic field is studied. The transition amplitude is formulated within the strong-field approximation in Göppert-Mayer gauge, with initial and final electron states being described by the corresponding Dirac-Coulomb and Dirac-Volkov wave functions, respectively. Coulomb corrections to the electron motion during tunneling are taken into account by adjusting an established method to the present situation. Total and energy-differential ionization rates are calculated and compared with predictions from other theories in a wide range of atomic numbers and applied field strengths.

The analytical R-matrix (ARM) theory has been known for an efficient description of the Coulomb effects of the atomic core in strong-field ionization in the nonrelativistic regime. We generalize the ARM theory into the relativistic domain aiming at the application to strong-field ionization of highly charged ions in ultrastrong laser fields. Comparison with the relativistic Coulomb-corrected strong-field approximations (SFA) is provided, highlighting the advantages and disadvantages. The weakly relativistic asymptotics and its accordance with the nondipole Coulomb-corrected SFA are examined. As an example of a physical application of the relativistic ARM, the Coulomb enhancement of tunneling ionization probability for highly charged ions at the cutoff of the direct channel is discussed.

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.

Tunneling ionization of an atom in ultrashort laser pulses is considered. When the driving laser pulse is switched-on and -off with a steep slope, the photoelectron momentum distribution (PMD) shows an edge-effect because of the photoelectron diffraction by the time-slit of the pulse. The trivial diffraction pattern of the edge effect consisting of fast oscillations in the PMD disguises in the deep nonadiabatic regime the physically more interesting features in the spectrum which originate from the photoelectron dynamics. We point out the precise conditions how to avoid this scenario experimentally and if unavoidable in theory we put forward an efficient method to remove the edge-effect in the PMD. This allows to highlight the nonadiabatic dynamical features of the PMD, which is indispensable for their further investigation in complex computationally demanding scenarios. The method is firstly demonstrated on a one-dimensional problem, and further applied in three-dimensions for the attoclock. The method is validated by a comparison of analytical results via the strong-field approximation with numerical solutions of the time-dependent Schr\"odinger equation.

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 generalised to include the leading light-front non-dipole Coulomb corrections and demonstrates the counter-intuitive 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 mid-infrared lasers.

The electron nondipole dynamics in tunneling ionization in an elliptically polarized laser field is investigated theoretically using a relativistic Coulomb-corrected strong-field approximation (SFA) based on the eikonal approximation of the Klein-Gordon equation. We calculate attoclock angle-resolved light-front momentum distributions at different ellipticities of the laser field in quasistatic and nonadiabatic regimes and analyze them with an improved simple man???s model. The nondipole correlations between longitudinal and transverse momentum components are examined. Deviations of the nondipole photoelectron momentum distribution calculated via SFA with respect to the available experimental results as well as with the improved simple man???s model are discussed and interpreted in terms of nonadiabatic as well as Coulomb effects in the continuum and under the barrier. The favorable prospects of an experimental observation are discussed.

The problem of time delay in tunneling ionization is revisited. The origin of time delay at the tunnel exit is analysed, underlining the two faces of the concept of the tunnelling time delay: the time delay around the tunnel exit and the asymptotic time delay at a detector. We show that the former time delay, in the sense of a delay in the peak of the wavefunction, exists as a matter of principle and arises due to the sub-barrier interference of the reflected and transmitted components of the tunneling electronic wavepacket. We exemplify this by describing the tunnelling ionization of an electron bound by a short-range potential within the strong field approximation in a "deep tunnelling" regime. If sub-barrier reflections are extracted from this wavefunction, then the time delay of the peak is shown to vanish. Thus, we assert that the disturbance of the tunnelling wavepacket by the reflection from the surface of the barrier causes a time delay in the neighbourhood of the tunnel exit.

The problem of Freeman resonances [Freeman et al., Phys. Rev. Lett. 59, 1092 (1987)] when strong-field ionization is enhanced due to transient population of excited Rydberg states during ionization is revisited. An intuitive model is put forward which explains the mechanism of intermediate population of excited states during nonadiabatic tunneling ionization via under-the-barrier recollision and recombination. The theoretical model is based on perturbative strong-field approximation (SFA), where the sub-barrier bound-continuum-bound pathway is described in the second-order SFA, with further ionization from the excited state by an additional perturbative step. The enhancement of ionization is shown to arise due to constructive interference of contributions into the excitation amplitudes originating from different laser cycles. The applied model provides an intuitive understanding of the electron dynamics during a Freeman resonance in strong-field ionization, as well as a means of enhancing the process and possible applications to related processes.

In strong-field ionization interferences between electron trajectories create a variety of interference structures in the final momentum distributions. Among them, the interferences between electron pathways that are driven directly to the detector and the ones that rescatter significantly with the parent ion lead to holography-type interference patterns that received great attention in recent years. In this work, we study the influence of the magnetic field component onto the holographic interference pattern, an effect beyond the electric dipole approximation, in experiment and theory. The experimentally observed nondipole signatures are analyzed via quantum trajectory Monte Carlo simulations. We provide explanations for the experimentally demonstrated asymmetry in the holographic interference pattern and its non-uniform photoelectron energy dependence as well as for the variation of the topology of the holography-type interference pattern along the laser field direction. Analytical scaling laws of the interference features are derived, and their direct relation to either the focal volume averaged laser intensities, or to the peak intensities are identified. The latter, in particular, provides a direct access to the peak intensity in the focal volume.