Relativistic and Ultrashort Quantum Dynamics
Since the invention of laser light amplification with chirped pulses, extremely short and strong laser fields have been generated with ever-increasing intensities. While current lasers reach up to 1022 W/cm2, the European Extreme-light-infrastructure (ELI) project aims at much higher fantastic intensities. A free-electron laser for a strong XUV radiation (FLASH facility) has been developed at DESY (Hamburg) where now a new x-ray free-electron laser (XFEL) is under construction. Another XFEL, LCLS (Linac Coherent Light Source) operates in SLAC (Stanford, USA). Moreover, experimentalists can produce well-controlled ultrashort and tailored laser pulses and carry out precise measurements of the electron and ion momenta in coincidence during strong-field ionization of atoms and molecules via a so-called reaction microscope. These achievements offer new methods for monitoring the bound electron dynamics with Angstrom spatial and attosecond temporal resolution, thus paving the way for efficient control of atomic and molecular processes in nanoscale. Thus, there is a bright outlook for the investigation of strong laser radiation interacting with matter, strong-field physics.
We investigate the interaction of strong laser radiation with matter. The systems under consideration range from free electrons, electron beams, single atoms/ions, few-atom ensembles, thin matter layers, and plasmas up to vacuum with quantum fluctuations. In the center of interest are the relativistic regimes of interaction. In particular, our attention is focused on nonlinear ionization dynamics in strong fields, as well as on radiative and nonlinear QED effects in strong fields. Our recent results include an understanding of the role of sub-barrier dynamics for shaping subtle features of the photoelectron momentum distribution in tunneling ionization, which shed light on the elusive notion of the tunneling time, as well as uncovers the signatures of the nondipole dynamics. In the direction of nonlinear QED during ultrastrong laser-electron beam interaction, we have recently put forward new methods for obtaining highly polarized electron and positron beams in femtosecond time scale using ultrastrong (but alternating) laser fields, as well as demonstrated efficient ways for transferring polarization from relativistic electrons to high-energy gamma-photons.
Selected results: Strong-field ionization
Signatures of under-the-barrier dynamics in tunneling ionization
In a strong laser field, ionization of an atom takes place via tunneling of the electron from the atomic bound state into the continuum through the potential barrier formed by the atomic potential and the laser field. Although the under-the-barrier dynamics is a small part of the whole laser-electron interaction in this process, it imprints its gentle signatures in the photoelectron momentum distribution at the detector. High resolution of momentum detection, better than 0.01 atomic units, is required to observe these signatures. One of these signatures is the time delay in the attoclock, see Fig. 1, which recently has been measured in a mixture of gases in . In the latter, the systematic experimental errors have been canceled by measuring the difference of the time delay for two gases. We have given successful theoretically explanations of these experimental results via the Wigner time delay during sub-barrier dynamics, see Fig. 2. While there are debates how to interpret the attoclock time delay, we put forward a simple straightforward interpretation in . The time delay is equivalent to a shift in the transverse momentum distribution of the attoclock, we have shown that the latter emerges when the interference of the direct ionization path with the under-the barrier recolliding one is accounted for, see Fig 3. We have also predicted another signature of the under-the-barrier dynamics due to the nondipole effect of the laser magnetic field . The peak of the electron momentum distribution along the laser propagation direction is shifted forward at the tunnel exit during the under-the barrier wave packet formation, Fig.4. It has a consequence for the photon momentum partition between the ion and the electron in the ionization process. Our fully relativistic prediction has been recently confirmed by an external group in ultra-high precision measurement in .
Interplay between Coulomb-focusing and nondipole effects in strong-field ionization with elliptical polarization
In collaboration with an experimental group of ETH, Zürich, we studied strong-field ionization and rescattering in the nondipole regime with elliptically polarized mid-IR laser pulses. An unexpected sharp ridge structure in the polarization plane in photoelectron momentum distribution (PMD) has been discovered , see Fig. Within a certain range of ellipticity, the electrons in this ridge are clearly separated from the two lobes that commonly appear in the PMD with elliptically polarized laser fields. In contrast to the well-known lobes of direct electrons, the sharp ridge is created by Coulomb focusing of the softly recolliding electrons. It appeared that this thin line-shaped ridge structure for low-energy photoelectrons is correlated with the ellipticity-dependent asymmetry of the PMD along the beam propagation direction. The peak of the projection of the PMD onto the beam propagation axis is shifted from negative to positive values when the sharp ridge fades away with increasing ellipticity . Our theoretical analysis  showed that the underlying physics is based on the interplay between the lateral drift of the ionized electron, the laser magnetic field induced drift in the laser propagation direction, and Coulomb focusing. The ellipticity-dependent 3D PMDs give access to different ionization and recollision dynamics with appropriate filters in the momentum space. For example, we can extract information about the spread of the initial wave packet and the Coulomb momentum transfer of the rescattering electrons.
Within the same collaboration, we have investigated also the influence of the laser magnetic-field component onto the holographic interference pattern  (the interferences between electron pathways that are driven directly to the detector and those that rescatter significantly with the parent ion lead to holography-type interference). We provided explanations for the experimentally demonstrated asymmetry in the holographic interference pattern and for the variation of the topology of the holography-type interference pattern along the laser-field direction.
Coulomb effects in strong-field processes
The Coulomb field of the atomic core plays a significant role in strong-field ionization. For a long time, it has been known that significant Coulomb effects arise at recollisions. While hard recollisions induce well-known processes of above-threshold ionization, high-order harmonic generation, and nonsequential double ionization, the soft recollisions bring about Coulomb focusing effect, which is responsible for the so-called, low-energy structures (LESs) in the photoelectron energy distribution at above threshold-ionization (ATI) in mid-infrared laser fields. We have explained the origin of the low-energy structure , which arises due to Coulomb focusing because of multiple forward scattering of the ionized electron by the parent ion, see Fig.1 A surprising fact was that the high-order scattering events have a nonperturbative comparable contribution to the total Coulomb focusing , and persist up to high ellipticity values of the driving laser field .
Recently, another surprising Coulomb field effect has been identified by ab initio numerical solution of time-dependent Schrödinger equation (TDSE): several orders enhancement of photoelectron spectra in the upper energy range of the direct electrons, i.e., at 2Up, twice the electron ponderomotive energy, has been observed. We have demonstrated  that the enhancement is of a classical origin. It is due to the longitudinal nonuniform Coulomb momentum transfer with respect to the ionization phase, which allows for the electrons tunneled not far from the peak of the laser field to accumulate at high energies, Fig.2. Moreover, our analysis reveals specific features of the angular distribution of high-energy direct electrons, which can be employed for molecular imaging.
The role of the Coulomb field for attoclock we have analyzed in  and showed that it is especially increased in the nonadiabatic regime. The latter is due to the closer tunnel exit coordinate to the atomic core in the nonadiabatic regime when the electron gains energy during tunneling.
Spin dynamics in relativistic ionization
Spin effects arise during the relativistic tunneling ionization process . We have investigated the spin-resolved ionization dynamics employing the relativistic Coulomb corrected dressed strong field approximation , and taking into account the laser field-driven electron spin dynamics in the bound state. Even if an electron is very tightly bound to an ionic core, it may still be crucially affected by a laser field of moderate intensity. Spin effects in the tunneling regime of ionization are built up in three steps: spin precession in the bound state, spin rotation during tunneling, and spin precession during the electron motion in the continuum, see Fig. The magnitude and scaling of the spin-flip and spin asymmetry effects at ionization are reduced when the electron spin dynamics in the bound state is taken into account. However, with super-strong laser fields, a large spin-flip effect is measurable when employing highly charged ions, initially polarized along the laser propagation direction. The anticipated spin-flip effect is expected to be measurable with modern laser techniques combined with an ion storage facility.
Relativistic high-order harmonic generation (HHG)
We have investigated the ways for extension of the ionization-recollision dynamics to the relativistic domain as a pathway to radiation sources in a hard x-ray domain via HHG. To this purpose, we consider different setups for the suppression of the magnetically induced drift in the relativistic regimes of HHG.
For example, the XUV or x-ray assistance can be employed to overcome the relativistic drift motion. Another possibility for relativistic HHG can be achieved by employing strong laser pulses tailored as an attosecond pulse train. The temporal tailoring of the laser pulse is intended to concentrate the ionizing and accelerating laser forces in short time intervals within the laser period, maintaining the average intensity of the pulse constant. This is because in the tailored laser pulse, fragments are avoided in the electron trajectory, in contrast to the sinusoidal laser pulse, where the electron acceleration is compensated by deceleration without a net energy gain by the electron, while the electron nevertheless continues to drift in the laser propagation direction. What appears particularly promising for the suppression of the relativistic drift is the use of an HHG scheme with counter-propagating attosecond pulse trains where a special method for phase-matching has been developed. The review of different schemes is given in .
Selected results: nonlinear QED
Laser-induced polarization of electron and positron beams
Relativistic polarized electron and positron beams are fundamental experimental tools to test symmetry properties in physics. Recently we have shown a way to polarize an electron and positron beams with currently available realistic laser fields . Nonlinear interaction of electrons with an elliptically polarized laser field has been shown to result in splitting of the beam with respect to polarization due to the spin dependence of radiation reaction, see Fig. 1. The latter is a consequence of the asymmetry of the photon emission probabilities with respect to the electron spin in the given laser field with a small ellipticity and yields up to 70% polarization. The asymmetry is particularly significant in high-energy photon spectra and can be employed for the polarization detection of a high-energy electron beam with extraordinary precision, with currently available strong laser fields . This method demonstrates a method of single-shot determination of polarization for ultrarelativistic electron beams via nonlinear Compton scattering.
Furthermore, in strong external fields, the electron-positron pair production probabilities possess much higher asymmetry with respect to the spin of the created particles than the radiation. The latter property is harnessed for the generation of highly polarized positrons in a two-color laser field possessing a high degree of asymmetry , see Fig. 2, and in a laser field with a small ellipticity . The pair generation is a nonlinear process, which is strongly suppressed in the minor cycle of the asymmetric laser field. As a result, the asymmetry of the laser pulse causes up to 60% polarization of the generated positrons.
Generation of circularly polarized (CP) and linearly polarized (LP) γ-rays via the single-shot interaction of an ultraintense laser pulse with a spin-polarized counterpropagating ultrarelativistic electron beam has been demonstrated in nonlinear Compton scattering in the quantum radiation-dominated regime . We show efficient ways for the transfer of the electron polarization to the high-energy photon polarization. In particular, multi-GeV CP (LP) γ- rays with the polarization of up to about 95% can be generated by a longitudinally (transversely) spin-polarized electron beam, with a photon flux meeting the requirements of recent proposals for the vacuum birefringence measurement in ultrastrong laser fields.
Gamma-rays with ultrastrong laser and electron beam interaction
The feasibility of the generation of bright ultrashort gamma-ray pulses we have demonstrated in the interaction of a relativistic electron bunch with a counterpropagating tightly focused superstrong laser beam in the radiation-dominated regime . Ultrashort gamma-ray bursts of hundreds of attoseconds and of dozens of megaelectronvolt photon energies in the near-backward direction of the initial electron motion can be generated, see Fig. 1, which is due to the tightly focused laser field structure and the radiation reaction. Interesting is that the duration of the gamma-ray burst is independent of the duration of the electron bunch and of the laser pulse.
Radiation of an electron bunch in a superstrong focused ultrashort laser pulse of variable duration can provide signatures of quantum radiation reaction . These are visible in the qualitative behavior of both the angular spread and the spectral bandwidth of the radiation spectra. The signatures are robust with respect to the variation of the electron and laser-beam parameters in a large range. In the same setup, we have identified a CEP effect specific to the ultrarelativistic regime . When the electron beam counterpropagates with the laser pulse, pronounced high-energy x-ray double peaks emerge near the backward direction relative to the initial electron motion, Fig.2. This is achieved in the relativistic interaction domain, where both the electron energy is required to be lower than for the electron reflection condition at the laser peak and the stochasticity effects in the photon emission need to be weak. The asymmetry parameter of the double peaks in the angular radiation distribution is shown to serve as a sensitive measure for the CEP of up to 10-cycle long laser pulses and can be applied for the characterization of extremely strong laser pulses in present and near future laser facilities.
Gamma-ray beams with a large angular momentum may affect astrophysical phenomena, which calls for appropriate earth-based experimental investigations. For this purpose, we have investigated  the generation of well-collimated gamma-ray beams with a very large orbital angular momentum using nonlinear Compton scattering of a strong laser pulse of twisted photons at ultrarelativistic electrons Fig.3. Angular momentum conservation among absorbed laser photons, quantum radiation, and electrons is numerically demonstrated in the quantum radiation-dominated regime. We point out that the angular momentum of the absorbed laser photons is not solely transferred to the emitted gamma photons, but due to radiation reaction shared between the gamma photons and interacting electrons. The accompanying process of electron-positron pair production is furthermore shown to enhance the orbital angular momentum gained by the gamma-ray beam.
High-energy electron-positron collider
For the high energy domain of laser physics, we have proposed the concept of a laser-driven high-energy electron-positron collider which employs a bunch of positronium atoms [1,2], see Fig. 1, or electron-positron created from vacuum . Ultraintense laser pulses are applied to combine in one single-femtosecond stage the electron and positron acceleration and their microscopic coherent collision in the GeV regime. We have shown that such coherent collisions yield a largely enhanced luminosity compared to conventional incoherent colliders, so that particle physics reaction with high-power lasers become possible. As an example, the feasibility of muon pair production from a positronium gas in a strong laser field has been investigated, see Fig. 2. By investigating the laser-dressed polarization operator , we identify a new contribution describing high-energy recollisions experienced by an electron-positron pair generated by pure light when a gamma photon impinges on an intense, linearly polarized laser pulse. The energy absorbed in the recollision process over the macroscopic laser wavelength corresponds to a large number of laser photons and can be exploited to prime high-energy reactions.