## 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 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 \96 LCLS (Linac Coherent Light Source) operates in SLAC (Stanford, USA). Moreover, experimentalists are able to produce well-controlled ultrashort and tailored laser pulses which offer efficient control over the bound electron dynamics, thus paving the way for attosecond spectroscopy. Thus, there is a bright outlook for the investigation of strong laser radiation interacting with matter, strong field physics. Among recent achievements are the production of few cycle laser pulses, attosecond pulses of XUV radiation, production of coherent ultraviolet radiation via self-amplified spontaneous emission in FEL as well as monoenergetic GeV electrons and MeV ions via laser-plasma interaction.

We investigate the interaction of strong laser radiation with matter. The systems under consideration range from free electrons, 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 and on radiative effects in strong fields, such as high-order harmonic generation (HHG) via free electrons, atomic systems, and plasmas.

As regards atomic systems, we have investigated, in particular, the role of relativistic effects during the under-the-barrier dynamics, and its implication for the tunneling time and spin effects. An interesting finding was that even during the short time of tunneling, relativistic effects arise imprinting their signatures on the electron dynamics. Thus, the relativistic effects allow to map the, so-called, tunneling time (Wigner time) into the shift in space distribution of the ionized electron wave packet and the, so-called, tunneling formation time (Keldysh time) into the shift of the electron momentum distribution.

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 .

The role of Coulomb field effects in strong field physics is also investigated. We have explained the origin of the low-energy structure in the photoelectron energy distribution at above threshold-ionization (ATI) in mid-infrared laser fields. It appears that the low-energy structure arises due to Coulomb focusing because of multiple forward scattering of the ionized electron by the parent ion. 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.

During the interaction of a strong laser radiation with electrons, the radiation reaction can play an important role in the relativistic regime. Unlike in the nonrelativistic case, a situation can occur in the ultrarelativistic regime in which the radiation reaction force becomes comparable with the Lorentz force in the laboratory frame while being much smaller in the instantaneous rest frame of the electron. This is the so-called radiation dominated regime in which the electron dynamics and its radiation are supposed to be significantly modified due to the radiation reaction. We have investigated the signatures of radiation reaction in the classical and quantum regimes of radiation in a strong laser field. Moreover, we have shown that the radiation reaction can significantly enhance the Raman scattering of a strong laser radiation in plasma due to the induced nonlinear mixing of the Stocks and anti-Stocks sidebands.

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. 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 reactions 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.

Super-strong laser fields offer unique possibilities for the investigation of the quantum vacuum. Different effects of vacuum QED nonlinearities induced by strong laser fields have been considered. The experimental observation of elastic photon-photon scattering is quite feasible for experimental observation as our analysis shows. Using a setup of multiple crossed superstrong laser beams the photon-photon scattering rate can be significantly enhanced due to Bragg interference. We have investigated the role of diffraction on the birefringence effects arising from the nonlinear interaction of an x-ray probe with a tightly focused standing laser wave. It turned out that the diffraction is unavoidable in a conventional experimental setup decreasing the birefringence effect by an order of magnitude. Nevertheless, the latter will, in principle, be technically measurable in the near future.

## Atomic quantum dynamics in the relativistic regime

### Relativistic features of the under-the-barrier dynamics in laser-induced ionization

We have investigated the role of relativistic effects during the under-the-barrier dynamics in laser-induced ionization. An interesting finding was that even during this short time before the release of the electron from the bound state, relativistic effects arise imprinting their signature on the electron dynamics and characteristics.\A0 An intuitive picture for the relativistic tunneling regime is developed demonstrating that the tunneling picture applies also in the relativistic case by introducing position dependent energy levels. The quantum dynamics in the classically forbidden region features two time scales, the typical time that characterizes the probability density\92s decay of the ionizing electron under the barrier (Keldysh time) and the time interval which the electron wave packet spends inside the barrier (Eisenbud-Wigner-Smith tunneling time). In the relativistic regime, an electron momentum shift as well as a spatial shift of the ionized electron wave packet along the laser propagation direction arise during the under-the-barrier motion which are caused by the laser magnetic field induced Lorentz force. The momentum shift is proportional to the Keldysh time, while the wave-packet\92s spatial drift is proportional to the Eisenbud-Wigner-Smith time. The signature of the momentum shift is shown to be present in the ionization spectrum at the detector and, therefore, observable experimentally, see Fig. 1. In contrast, the signature of the Eisenbud-Wigner-Smith time delay disappears at far distances for pure tunneling dynamics [1,2].

**[1]****M. Klaiber, E. Yakaboylu, H. Bauke, K. Z. Hatsagortsyan, and C. H. Keitel, Phys. Rev. Lett. 110, 153004 (2013); arXiv:1205.2004v1 [physics.atom-ph]**

**[2] E. Yakaboylu, M. Klaiber, H. Bauke, K. Z. Hatsagortsyan and C. H. Keitel,\A0 arXiv:1309.0610 [quant-ph]**