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General formulation in the realm of strong-field quantum electrodynamics is provided for a process that occurs in the presence of a train of laser pulses and, in the tree level, is represented by a two-vertex Feynman diagram with exchange of a virtual photon. A scheme of retrieving resonances in the corresponding probability distributions is also formulated in these general settings. While the presented formalism is applicable to a variety of processes like electron-positron pair creation and annihilation, M\"oller scattering, Bhabha scattering, etc., we illustrate it for a trident process. Specifically, we consider electron-positron pair creation in the muon--laser-field collisions. We demonstrate that the probability distributions exhibit integrable singularities close to the threshold of pair creation. Also, a variety of resonances is observed that originate from the poles of the Feynman photon propagator. While those resonances are, in general, obscured by strong quantum interferences, we show that they can be isolated by changing the carrier envelope phase of the driving laser pulses. In that case, while transformed into the Lorentz-Breit-Wigner shape profile, the resonance position and width can be determined., Comment: 15 pages, 9 figures

General formulation in the realm of strong-field quantum electrodynamics is provided for a process that occurs in the presence of a train of laser pulses and, in the tree level, is represented by a two-vertex Feynman diagram with exchange of a virtual photon. A scheme of retrieving resonances in the corresponding probability distributions is also formulated in these general settings. While the presented formalism is applicable to a variety of processes like electron-positron pair creation and annihilation, M\"oller scattering, Bhabha scattering, etc., we illustrate it for a trident process. Specifically, we consider electron-positron pair creation in the muon--laser-field collisions. We demonstrate that the probability distributions exhibit integrable singularities close to the threshold of pair creation. Also, a variety of resonances is observed that originate from the poles of the Feynman photon propagator. While those resonances are, in general, obscured by strong quantum interferences, we show that they can be isolated by changing the carrier envelope phase of the driving laser pulses. In that case, while transformed into the Lorentz-Breit-Wigner shape profile, the resonance position and width can be determined., Comment: 15 pages, 9 figures

Dynamical Sauter-Schwinger mechanism of pair creation by a time-dependent electric field comprising of $N_{\rm rep}$ identical pulses is analyzed within the framework of the spinor and scalar quantum electrodynamics. For linearly polarized pulses, both theories predict that a single eigenmode of the matter wave follows the dynamics of a two-level system. This dynamics, however, is either governed by a Hermitian (for spin 1/2 particles) or pseudo-Hermitian (for spin 0 particles) Hamiltonian. Essentially, both theories lead to a Fraunhofer-type enhancement of the momentum distributions of created pairs. While in the fermionic case the enhancement is never perfect and it deteriorates with increasing the number of pulses in a train $N_{\rm rep}$, in the bosonic case we observe the opposite. More specifically, it is at exceptional points where the spectra of bosonic pairs scale exactly as $N_{\rm rep}^2$, and this scaling is even enhanced with increasing the number of pulses in a train., Comment: 30 pages, 8 figures

Momentum distributions of electron-positron pairs created from the vacuum by an oscillating in time electric field are calculated in the framework of quantum field theory. A pronounced enhancement of those distributions is observed as the frequency of the electric field passes across the one-photon threshold. Below that threshold the pairs preferentially carry a longitudinal momentum, while above the threshold they tend to carry a transverse momentum. Such momentum sharing has an impact on the number of produced pairs: It grows fast with increasing the field frequency below the threshold but it saturates at a roughly constant value above it. On the other hand, at the fixed frequency above the one-photon threshold, the number of pairs scales quadratically with the field strength. This typically perturbative scaling holds even for large electric fields. Thus, the validity of the perturbation theory is extended here to processes which result in creation of particles with substantial transverse momenta., Comment: 8 pages, 8 figures

The Sauter-Schwinger process of electron-positron pair creation from vacuum, driven by a sequence of time-dependent electric-field pulses, is studied in the framework of quantum-field theoretical approach. As demonstrated by our numerical results, the probability distributions of produced pairs exhibit intra- and inter-pulse interference structures. We show that such structures can be observed beyond the regime of applicability of the WKB theory, which was the focus of earlier investigations. Going beyond these developments, we perform the analysis of the time-evolution operator for an arbitrary eigenmode of the fermionic field. This shows that a perfect coherent enhancement of the inter-pulse peaks can never be reached. A nearly perfect coherence, on the other hand, is due to nonadiabatic transitions at avoided crossings of the phases defining the unitary time evolution. This analysis allows us to determine the conditions under which the nearly perfect coherence is lost., Comment: 13 pages, 6 figures

Ionization of hydrogen-like ions by intense, circularly polarized laser pulses is analyzed under the scope of the relativistic strong-field approximation. We show that, for specific parameters of the laser field, the energy spectra of photoelectrons present a broad region without interference (supercontinuum) which can be controlled by modifying the laser field intensity. The physical interpretation of the process is developed according to the Keldysh theory, emphasizing the importance of the complex-time saddle point contributions to the total probability of photoionization. The corresponding polar-angle distributions present an asymmetry attributed to radiation pressure effects., Comment: 8 pages, 5 figures

Production of electron-positron pairs in the collision of a high-energy photon with a high-intensity few-cycle laser pulse is studied. By utilizing the frameworks of laser-dressed spinor and scalar quantum electrodynamics, a comparison between the production of pairs of Dirac and Klein-Gordon particles is drawn. Positron energy spectra and angular distributions are presented for various laser parameters. We identify conditions under which predictions from Klein-Gordon theory either closely resemble or largely differ from those of the proper Dirac theory. In particular, we address the question to which extent the relevance of spin effects is influenced by the short duration of the laser pulse., Comment: 11 pages, 7 figures

The eikonal perturbation theory is formulated and applied to photoionization by strong laser pulses. A special emphasis is put on the first order approximation with respect to the binding potential, which is known as the generalized eikonal approximation [2015 Phys. Rev. A 91 053417]. The ordinary eikonal approximation and its domain of applicability is derived from the generalized eikonal approximation. While the former approach is singular for the electron trajectories which return to the potential center, the generalized eikonal avoids this problem. This property makes it a promising tool for further investigations of rescattering and high-order harmonic generation processes.

The concept of the electron mass dressing by a powerful laser pulse is discussed. It is shown, by considering the coherent frequency combs generated out of the Compton radiation, how the electron dressed mass can be determined experimentally. This also opens a possibility to measure properties of extremely intense pulses for which the previously developed methods, working at moderate intensities, are not applicable. Namely, one can determine these properties from the properties of coherent Compton radiation., Comment: 7 pages, 4 figures; lecture delivered during the 24th International Laser Physics Workshop, Shanghai, August 21-25, 2015

The generalized Klein-Nishina formula for Compton scattering of charged particles by a finite train of pulses is derived in the framework of quantum electrodynamics. The formula also applies to classical Thomson scattering provided that frequencies of generated radiation are smaller that the cut-off frequency. The validity of the formula for incident pulses of different durations is illustrated by numerical examples. The positions of the well-resolved Compton peaks, with the clear labeling by integer orders, opens up the possibility of the precise diagnostics of properties of relativistically intense, short laser pulses. This includes their peak intensity, the carrier-envelope phase, and their polarization properties., Comment: 9 pages, 6 figures

Electron-positron pair creation in collisions of a modulated laser pulse with a high-energy photon (nonlinear Breit-Wheeler process) is studied by means of strong-field quantum electrodynamics. It is shown that the driving pulse modulations lead to appearance of comb structures in the energy spectra of produced positrons (electrons). It is demonstrated that these combs result from a coherent enhancement of probability amplitudes of pair creation from different modulations of the laser pulse. Thus, resembling the Young-double slit experiment for anti-matter (matter) waves., Comment: 9 pages, 5 figures

The Compton and Thomson radiation spectra, generated in collisions of an electron beam with a powerful laser beam, are studied in the framework of quantum and classical electrodynamics, respectively. We show that there are frequency regimes where both radiation spectra are nearly identical, which for Compton scattering relates to the process which preserves the electron spin. Although the radiation spectra are nearly identical, the corresponding probability amplitudes exhibit different global phases. This has pronounced consequences, which we demonstrate by investigating temporal power distributions in both cases. We show that, contrary to Thomson scattering, it is not always possible to synthesize short laser pulses from Compton radiation. This happens when the global phase of the Compton amplitude varies in a nonlinear way with the frequency of emitted photons. We also demonstrate that while the Compton process driven by a non-chirped laser pulse can generate chirped bursts of radiation, this is not the case for the Thomson process. In principle, both processes can lead to a generation of coherent frequency combs when single or multiple driving laser pulses collide with electrons. Once we synthesize these combs into short bursts of radiation, we can control them, for instance, by changing the time delay between the driving pulses., Comment: 18 pages, 15 figures

Nonlinear Thomson and Compton processes, in which energetic electrons collide with an intense optical pulse, are investigated in the framework of classical and quantum electrodynamics. Spectral modulations of the emitted radiation, appearing as either oscillatory or pulsating structures, are observed and explained. It is shown that both processes generate a bandwidth radiation spanning the range of few MeV, which occurs in a small cone along the propagation direction of the colliding electrons. Most importantly, these broad bandwidth structures are temporarily coherent which proves that Thomson and Compton processes lead to generation of a supercontinuum. It is demonstrated that the radiation from the supercontinuum can be synthesized into zeptosecond (possibly even yoctosecond) pulses. Thus, confirming that Thomson and Compton scattering can be used as novel sources of an ultra-short radiation, opening routes to new physical domains for strong laser physics., Comment: 10 pages, 11 figures

Spectra of Thomson and Compton radiation, emitted during electron scattering off an intense laser beam, are calculated using the frameworks of classical and strong-field quantum electrodynamics, respectively. Both approaches use a plane-wave-fronted pulse approximation regarding the driving laser beam. Within this approximation, a very good agreement between Thomson and Compton frequency distributions is observed provided that frequencies of the emitted radiation is relatively low. The dependence of frequency spectra on the laser pulse envelope is analyzed. This becomes important in the context of ultra-short pulse generation, as illustrated by numerical examples., Comment: 13 pages, 4 figures; lecture delivered during the 22nd International Laser Physics Workshop, Prague, July 15-19, 2013