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Quantum field theory predicts a nonlinear response of the vacuum to strong electromagnetic fields of macroscopic extent. This fundamental tenet has remained experimentally challenging and is yet to be tested in the laboratory. A particularly distinct signature of the resulting optical activity of the quantum vacuum is vacuum birefringence. This offers an excellent opportunity for a precision test of nonlinear quantum electrodynamics in an uncharted parameter regime. Recently, the operation of the high-intensity laser ReLaX provided by the Helmholtz International Beamline for Extreme Fields (HIBEF) has been inaugurated at the High Energy Density (HED) scientific instrument of the European XFEL. We make the case that this worldwide unique combination of an x-ray free-electron laser and an ultra-intense near-infrared laser together with recent advances in high-precision x-ray polarimetry, refinements of prospective discovery scenarios, and progress in their accurate theoretical modelling have set the stage for performing an actual discovery experiment of quantum vacuum nonlinearity., Comment: 34 pages, 21 figures

We present a theoretical framework based on second quantization in Liouville space to treat open quantum systems. We consider an ensemble of identical quantum emitters characterized by a discrete set of quantum states. The second quantization is performed directly at the level of density matrices, thereby significantly reducing the size of the Liouville space. In contrast to conventional Hilbert space techniques, statistically mixed states and dissipation are naturally incorporated. As a particular example of application, we study the effect of incoherent processes and statistical mixing of emitters' initial states in the interaction with quantum light. Moreover, we link our framework to a phase-space description of the dynamics, which can overcome the computational limitations of our method with the increasing number of particles., Comment: 14 pages, 3 figures

We report on the observation of time-resolved quantum beats in the helium fluorescence from the transition 1s3p -> 1s2s, where the initial state is excited by XUV free-electron laser radiation. The quantum beats originate from the Zeeman splitting of the magnetic substates due to an external magnetic field. We perform a systematic study of this effect and discuss the possibilities of studying this phenomenon in the XUV and x-ray regime., Comment: 7 pages, 4 figures

Oscillators are at the heart of optical lasers, providing stable transform limited pulses. In contrast, X-ray free electron lasers use self-amplified spontaneous emission (SASE), resulting in large stochastic intensity and spectral fluctuations. Amplified spontaneous emission (ASE) of the $K\alpha_1$ line has been recently observed for Ne gas, Cu compounds and Mn solutions at the LCLS and SACLA X-ray free electron lasers (XFELs), using an X-ray SASE pulse as a pump to create population inversion. Here we describe the physics and realization of an X-ray laser oscillator (XLO) based on periodically pumping a Cu compound gain medium in a tunable Bragg cavity with a SASE pulse train, generating intense ($\sim$ 5 x 10$^{10}$ ph/pulse), fully coherent, transform limited 8 keV pulses with 48 meV spectral resolution. We also discuss extending these results to other elements to operate XLO from about 5 to 12 keV, improving X-ray-based research beyond current capabilities.

We present a comprehensive experimental and theoretical study on superfluorescence in the extreme ultraviolet wavelength regime. Focusing a high-intensity free-electron laser pulse in a cell filled with Xe or Kr gas, the medium is quasi instantaneously population-inverted by inner-shell ionization on the giant resonance followed by Auger decay. On the timescale of 100 ps a macroscopic polarization builds up in the medium, resulting in superfluorescent emission of several Xe and Kr lines in the forward direction. As the number of emitters in the system is increased by either raising the pressure or the pump-pulse energy, the emission shows an exponential growth of over 4 orders of magnitude and reaches saturation. With increasing yield, we observe line broadening, a manifestation of superfluorescence in the spectral domain. Our novel theoretical approach, based on a full quantum treatment of the atomic system and the irradiated field, shows quantitative agreement with the experiment and supports our interpretation.

We introduce and demonstrate a new approach to measuring coherent electron wave packets using high-harmonic spectroscopy. By preparing a molecule in a coherent superposition of electronic states, we show that electronic coherence opens previously unobserved high-harmonic-generation channels that connect distinct but coherently related electronic states. Performing the measurements in dynamically aligned nitric oxide (NO) molecules we observe the complex temporal evolution of the electronic coherence under coupling to nuclear motion. Choosing a weakly allowed transition to prepare the wave packet, we demonstrate an unprecedented sensitivity that arises from optical interference between coherent and incoherent pathways. This mechanism converts a 0.1 $%$ excitation fraction into a $\sim$20 $%$ signal modulation.

We investigate the heating of the quasi-free electrons in large rare gas clusters (N exceeding 10^5 atoms) by short laser pulses at moderate intensities (I~10^{15} Wcm^{-2}). We identify elastic large-angle backscattering of electrons at ionic cores in the presence of a laser field as an efficient heating mechanism resembling the Fermi shuttle. Its efficiency as well as the effect of collective electron motion, electron-impact ionization and cluster charging, are studied employing a mean-field classical transport simulation. Results for the absolute x-ray yields are in surprisingly good quantitative agreement with recent experimental results., Comment: 5 pages,4 figures, submitted to Phys. Rev. Lett

We present an extension of the modular recursive Green's function method (MRGM) for ballistic quantum transport to include magnetic fields. Dividing the non-separable two-dimensional scattering problem into separable substructures allows us to calculate transport coefficients and scattering wavefunctions very efficiently. Previously unattainable energy and magnetic field regions can thereby be covered with high accuracy. The method is applied to magnetotransport through a circle and a stadium shaped quantum dot at strong magnetic fields and high energies. In the edge state regime we observe strong multi-frequency Aharonov-Bohm oscillations. By analyzing them in terms of a multi-channel interference model, we classify these fluctuations within the framework of Fano resonances and discuss their geometry independence. For high energies (mode numbers) we observe localization of the scattering wavefunction near classical trajectories., Comment: 20 pages, 10 figures, to appear in Phys.Rev.B