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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

Above-threshold ionization spectra from cesium are measured as a function of the carrier-envelope phase (CEP) using laser pulses centered at 3.1 $\mu$m wavelength. The directional asymmetry in the energy spectra of backscattered electrons oscillates three times, rather than once, as the CEP is changed from $0$ to $2\pi$. Using the improved strong-field approximation, we show that the unusual behavior arises from the interference of few quantum orbits. We discuss the conditions for observing the high-order CEP dependence, and draw an analogy with time-domain holography with electron wave packets.

Production of electron-positron pairs from vacuum in strong bichromatic electric fields, oscillating in time with a fundamental frequency and its second harmonic, is studied. Strong-field processes occuring in such field configurations are generally known to be sensitive to the relative phase between the field modes. Phase-of-the-phase spectroscopy has recently been introduced in the context of strong-field photoionization as a systematic means to analyze these coherence effects. We apply this method to field-induced pair production by calculating the phase dependence of the momentum-resolved particle yields. We show that asymmetric checkerboard patterns arise in the phase-of-the-phase spectra, similarly to those found in strong-field photoionization. The physical origin of these characteristic structures, which differ between the created electron and positron, are discussed., Comment: 8 pages, 6 figures

An electrical pulse E(t) is completely defined by its time-dependent amplitude and polarisation direction. For optical pulses the manipulation and characterisation of the light polarisation state is fundamental due to its relevance in several scientific and technological fields. In this work we demonstrate the complete temporal reconstruction of the electric field of few-cycle pulses with a complex time-dependent polarisation. Our experimental approach is based on extreme ultraviolet interferometry with isolated attosecond pulses and on the demonstration that the motion of an attosecond electron wave packet is sensitive to perturbing fields only along the direction of its motion. By exploiting the sensitivity of interferometric techniques and by controlling the emission and acceleration direction of the wave packet, pulses with energies as low as few hundreds of nanojoules can be reconstructed. Our approach opens the possibility to completely characterise the electric field of the pulses typically used in visible pump-probe spectroscopy.

Utilizing a benchmark measurement of laser-induced ionization of an H$_2^+$ molecular ion beam target at infrared wavelength around 2 $\mu$m, we show that the characteristic two-peak structure predicted for laser-induced enhanced ionization of H$_2^+$ and diatomic molecules in general, is a phenomenon which is confined to a small laser parameter space --- a Goldilocks Zone. Further, we control the effect experimentally and measure its imprint on the electron momentum. We replicate the behavior with simulations, which reproduce the measured kinetic-energy release as well as the correlated-electron spectra. Based on this, a model, which both maps out the Goldilocks Zone and illustrates why enhanced ionization has proven so elusive in H$_2^+$, is derived., Comment: 5 pages, 4 figures

We demonstrate the complete reconstruction of the electric field of visible-infrared pulses with energy as low as a few tens of nanojoules. The technique allows for the reconstruction of the instantaneous electric field vector direction and magnitude, thus giving access to the characterisation of pulses with an arbitrary time-dependent polarisation state. The technique combines extreme ultraviolet interferometry with the generation of isolated attosecond pulses., Comment: 5 figures

The laser-induced fragmentation dynamics of this most fundamental polar molecule HeH$^+$ are measured using an ion beam of helium hydride and an isotopologue at various wavelengths and intensities. In contrast to the prevailing interpretation of strong-field fragmentation, in which stretching of the molecule results primarily from laser-induced electronic excitation, experiment and theory for nonionizing dissociation, single ionization and double ionization both show that the direct vibrational excitation plays the decisive role here. We are able to reconstruct fragmentation pathways and determine the times at which each ionization step occurs as well as the bond length evolution before the electron removal. The dynamics of this extremely asymmetric molecule contrast the well-known symmetric systems leading to a more general picture of strong-field molecular dynamics and facilitating interpolation to systems between the two extreme cases., Comment: new version includes minore changes and adding the supp_material.pdf

Energy coupling during relativistically intense laser-matter interactions is encoded in the attosecond motion of strongly driven electrons at the pre-formed plasma-vacuum boundary. Studying and controlling this motion can reveal details about the microscopic processes that govern a vast array of light-matter interaction physics and applications. These include research areas right at the forefront of extreme laser-plasma science such as laser-driven ion acceleration1, bright attosecond pulse generation2,3 and efficient energy coupling for the generation and study of warm dense matter4. Here we demonstrate attosecond control over the trajectories of relativistic electron bunches formed during such interactions by studying the emission of extreme ultraviolet (XUV) harmonic radiation. We describe how the precise addition of a second laser beam operating at the second harmonic of the driving laser pulse can significantly transform the interaction by modifying the accelerating potential provided by the fundamental frequency to drive strong coherent emission. Numerical particle-in-cell code simulations and experimental observations demonstrate that this modification is extremely sensitive to the relative phase of the two beams and can lead to significant enhancements in the resulting harmonic yield. This work also reveals that the ability to control these extreme interactions with attosecond precision is an essential requirement for generation of ultra-bright, high temporal contrast attosecond radiation for atomic and molecular pump-probe experiments5,6.

We present a momentum-resolved study of strong field multiple ionization of ionic targets. Using a deconvolution method we are able to reconstruct the electron momenta from the ion momentum distributions after multiple ionization up to four sequential ionization steps. This technique allows an accurate determination of the saturation intensity as well as of the electron release times during the laser pulse. The measured results are discussed in comparison to typically used models of over-the-barrier ionization and tunnel ionization.

Group velocity control is demonstrated for x-ray photons of 14.4 keV energy via a direct measurement of the temporal delay imposed on spectrally narrow x-ray pulses. Sub-luminal light propagation is achieved by inducing a steep positive linear dispersion in the optical response of ${}^{57}$Fe M\"ossbauer nuclei embedded in a thin film planar x-ray cavity. The direct detection of the temporal pulse delay is enabled by generating frequency-tunable spectrally narrow x-ray pulses from broadband pulsed synchrotron radiation. Our theoretical model is in good agreement with the experimental data., Comment: 8 pages, 4 figures

We report the enhancement of individual harmonics generated at a relativistic ultra-steep plasma vacuum interface. Simulations show the harmonic emission to be due to the coupled action of two high velocity oscillations -- at the fundamental $\omega_L$ and at the plasma frequency $\omega_P$ of the bulk plasma. The synthesis of the enhanced harmonics can be described by the reflection of the incident laser pulse at a relativistic mirror oscillating at $\omega_L$ and $\omega_P$., Comment: 5 pages, 3 figures. arXiv admin note: substantial text overlap with arXiv:1307.5635

We present few-femtosecond shadowgraphic snapshots taken during the non-linear evolution of the plasma wave in a laser wakefield accelerator with transverse synchronized few-cycle probe pulses. These snapshots can be directly associated with the electron density distribution within the plasma wave and give quantitative information about its size and shape. Our results show that self-injection of electrons into the first plasma wave period is induced by a lengthening of the first plasma period. Three dimensional particle in cell simulations support our observations., Comment: 5 pages, 4 figures

Waveform shaping and frequency synthesis based on waveform modulation is ubiquitous in electronics, telecommunication technology, and optics. For optical waveforms, the carrier frequency is on the order of several hundred THz, while the modulation frequencies used in conventional devices like electro- or acousto-optical modulators are orders of magnitude lower. As a consequence, any new frequencies are typically very close to the fundamental. The synthesis of new frequencies in the extreme ultraviolet (XUV), e.g. by using relativistic oscillating mirrors, requires modulation frequencies in the optical regime or even in the extreme ultraviolet. The latter has not been proven possible to date. Here we demonstrate that individual strong harmonics can indeed be generated by reflecting light off a plasma surface that oscillates at XUV frequencies. The strong harmonics are explained by nonlinear frequency mixing of near-infrared light and a laser-driven plasma oscillation in the extreme ultra-violet mediated by a relativistic non-linearity., Comment: 17 pages, 4 figures

Measurements and calculations of the absolute carrier-envelope phase (CEP) effects in the photodissociation of the simplest molecule, H2+, with a 4.5-fs Ti:Sapphire laser pulse at intensities up to (4 +- 2)x10^14 Watt/cm^2 are presented. Localization of the electron with respect to the two nuclei (during the dissociation process) is controlled via the CEP of the ultra-short laser pulses. In contrast to previous CEP-dependent experiments with neutral molecules, the dissociation of the molecular ions is not preceded by a photoionization process, which strongly influences the CEP dependence. Kinematically complete data is obtained by time- and position-resolved coincidence detection. The phase dependence is determined by a single-shot phase measurement correlated to the detection of the dissoziation fragments. The experimental results show quantitative agreement with ab inito 3D-TDSE calculations that include nuclear vibration and rotation., Comment: new version includes minore changes and adding the supp_material.pdf

We propose three implementations of the Gauss sum factorization schemes discussed in part I of this series: (i) a two-photon transition in a multi-level ladder system induced by a chirped laser pulse, (ii) a chirped one-photon transition in a two-level atom with a periodically modulated excited state, and (iii) a linearly chirped one-photon transition driven by a sequence of ultrashort pulses. For each of these quantum systems we show that the excitation probability amplitude is given by an appropriate Gauss sum. We provide rules how to encode the number N to be factored in our system and how to identify the factors of N in the fluorescence signal of the excited state., Comment: 22 pages, 7 figures

Experimental results from the generation of Raman sidebands using optical vortices are presented. By generating two sets of sidebands originating from different locations in a Raman active crystal, one set containing optical orbital angular momentum and the other serving as a reference, a Young's double slit experiment was simultaneously realized for each sideband. The interference between the two sets of sidebands was used to determine the helicity and topological charge in each order. Topological charges in all orders were found to be discrete and follow selection rules predicted by a cascaded Raman process., Comment: 4 pages, 3 figures

Asymmetric molecules look different when viewed from one side or the other. This difference influences the electronic structure of the valence electrons, thereby giving stereo sensitivity to chemistry and biology. We show that attosecond and re-collision science provides a detailed and sensitive probe of electronic asymmetry. On each 1/2 cycle of an intense light pulse, laser-induced tunnelling extracts an electron wave packet from the molecule. When the electron wave packet recombines, alternately from one side of the molecule or the other, its amplitude and phase asymmetry determines the even and odd harmonics radiation that it generates. This harmonic spectrum encodes three manifestations of asymmetry; an amplitude and phase asymmetry in electron tunneling; an asymmetry in the phase that the electron wave packet accumulates relative to the ion between the moment of ionization and recombination; and an asymmetry in the amplitude and phase of the transition moment. We report the first measurement of high harmonics from oriented gas samples. We determine the phase asymmetry of the attosecond XUV pulses emitted when an electron recollides from opposite sides of the CO molecule, and the phase asymmetry of the recollision electron just before recombination. We discuss how the various contributions to asymmetry can be isolated in future experiments., Comment: Contains SOM

The physics of high harmonics has led to the generation of attosecond pulses and to trains of attosecond pulses. Measurements that confirm the pulse duration are all performed in the far field. All pulse duration measurements tacitly assume that both the beam's wavefront and intensity profile are independent of frequency. However, if one or both are frequency dependent, then the retrieved pulse duration depends on the location where the measurement is made. We measure that each harmonic is very close to a Gaussian, but we also find that both the intensity profile and the beam wavefront depend significantly on the harmonic order. Thus, our findings mean that the pulse duration will depend on where the pulse is observed. Measurement of spectrally resolved wavefronts along with temporal characterization at one single point in the beam would enable complete space-time reconstruction of attosecond pulses. Future attosecond science experiments need not be restricted to spatially averaged observables.

We present experimental results for the ionization of aniline and benzene molecules subjected to intense ultrashort laser pulses. Measured parent molecular ions yields were obtained using a recently developed technique capable of three-dimensional imaging of ion distributions within the focus of a laser beam. By selecting ions originating from the central region of the focus, where the spatial intensity distribution is nearly uniform, volumetric-free intensity-dependent ionization yields were obtained. The measured data revealed a previously unseen resonant-like multiphoton ionization process. Comparison of benzene, aniline and Xe ion yields demonstrate that the observed intensity dependent structures are not due to geometric artifacts in the focus. Finally we attribute the ionization of aniline to a stepwise process going through the pi-sigma^star state which sits 3 photons above the ground state and 2 photons below the continuum., Comment: 18 pages, 1 equation and 3 figures

A new scheme for a double-slit experiment in the time domain is presented. Phase-stabilized few-cycle laser pulses open one to two windows (``slits'') of attosecond duration for photoionization. Fringes in the angle-resolved energy spectrum of varying visibility depending on the degree of which-way information are observed. A situation in which one and the same electron encounters a single and a double slit at the same time is discussed. The investigation of the fringes makes possible interferometry on the attosecond time scale. The number of visible fringes, for example, indicates that the slits are extended over about 500as., Comment: 4 figures

Numerical simulations on the evolution of step-screw and edge-screw optical phase dislocations in bulk saturable self-defocusing nonlinear media are presented, with emphasis on their ability to induce steering waveguides for signal beams (pulses). Two schemes for directional coupling of such signals, both ensuring reasonable coupling-to-cross-talk efficiency ratio, are investigated. The parameters useful for performance optimization of the couplers are discussed., Comment: 6 pages, 5 figures, 2 tables, submitted to Appl. Phys. B

Theoretical and experimental results on optical ring dark solitary waves are presented, emphasizing the interplay between initial dark beam contrast, phase-shift magnitude, background-beam intensity and saturation of the nonlinearity are presented. The results are found to confirm qualitatively the existing analytical theory and are in agreement with the numerical simulations carried out., Comment: 7 pages, 8 figures, submitted to PRE

In this work we report the first realization of odd dark beams of finite length under controllable initial conditions. The mixed edge-screw phase dislocations are obtained by reproducing binary computer-generated holograms. Two effective ways to control the steering of the beams are analyzed experimentally and compared with numerical simulations., Comment: 7 pages, 10 figure; Submited to JOSA B