Using a simple model of strong-field ionization of atoms that generalizes the well-known 3-step model from 1D to 3D, we show that the experimental photoelectron angular distributions resulting from laser ionization of xenon and argon display prominent structures that correspond to electrons that pass by their parent ion more than once before strongly scattering. The shape of these structures can be associated with the specific number of times the electron is driven past its parent ion in the laser field before scattering. Furthermore, a careful analysis of the cutoff energy of the structures allows us to experimentally measure the distance between the electron and ion at the moment of tunnel ionization. This work provides new physical insight into how atoms ionize in strong laser fields and has implications for further efforts to extract atomic and molecular dynamics from strong-field physics. DOI: 10.1103/PhysRevLett.109.073004 PACS numbers: 32.80.Fb, 32.80.Rm, 34.80.Qb When an atom or molecule is illuminated with a moderately intense femtosecond laser field ($ 10 14 W=cm 2 ), an electron wave packet will tunnel ionize and accelerate in the field before being turned around by the field and returning to the parent ion. The returning electron can either recombine with the parent ion, releasing its kinetic energy as a high-energy photon [1-3], or can elastically scatter from the potential of the ion. The photons and electrons generated by these strong-field processes have the potential to probe the dynamic structure of molecules and materials on the subnanometer length scale and femtosecond-to-attosecond time scale. Several recent papers have suggested that structures seen in angledependent photoelectron spectra may be useful for determining time-resolved molecular structures [4], characterizing attosecond electron wave packets [5], and studying the dynamics of electron wave packet propagation [6]. However, despite extensive analyses [7][8][9][10][11], many features observed in angle-resolved photoelectron spectra still lack a simple physical explanation.The recent development of midinfrared (mid-IR) femtosecond lasers [12] and angle-resolved detection schemes [13] has enabled new advances in visualizing strong-field physics. Electrons that are ionized in a mid-IR laser field reach higher velocities because of the larger ponderomotive energy, given by U P / I 2 , where I is the intensity and is the wavelength. The possibility of harnessing the high-energy electrons that are first ionized and then driven back to a molecule by a strong laser field has inspired several theoretical and experimental efforts to use strongfield ionization to probe molecular structure [4,[14][15][16]. Recently, Huismans and co-workers [17] used 7 m mid-IR lasers, in combination with angle-resolved detection, to observe angular interference structures in the photoelectron spectra. They presented a theoretical model that explains these structures based on the difference in the phase between two different paths that electrons can take to...

We demonstrate, to our knowledge, the first bright circularly polarized high-harmonic beams in the soft X-ray region of the electromagnetic spectrum, and use them to implement X-ray magnetic circular dichroism measurements in a tabletop-scale setup. Using counterrotating circularly polarized laser fields at 1.3 and 0.79 μm, we generate circularly polarized harmonics with photon energies exceeding 160 eV. The harmonic spectra emerge as a sequence of closely spaced pairs of left and right circularly polarized peaks, with energies determined by conservation of energy and spin angular momentum. We explain the single-atom and macroscopic physics by identifying the dominant electron quantum trajectories and optimal phasematching conditions. The first advanced phase-matched propagation simulations for circularly polarized harmonics reveal the influence of the finite phase-matching temporal window on the spectrum, as well as the unique polarization-shaped attosecond pulse train. Finally, we use, to our knowledge, the first tabletop X-ray magnetic circular dichroism measurements at the N 4,5 absorption edges of Gd to validate the high degree of circularity, brightness, and stability of this light source. These results demonstrate the feasibility of manipulating the polarization, spectrum, and temporal shape of high harmonics in the soft X-ray region by manipulating the driving laser waveform.X-rays | high harmonics generation | magnetic material | ultrafast light science | phase matching H igh-harmonic generation (HHG) results from an extreme nonlinear quantum response of atoms to intense laser fields. When implemented in a phase-matched geometry, bright, coherent HHG beams can extend to photon energies beyond 1.6 keV (1, 2). For many years, however, bright HHG was limited to linear polarization, precluding many applications in probing and characterizing magnetic materials and nanostructures, as well as chiral phenomena in general. Although X-ray optics can in principle be used to convert extreme UV (EUV) and X-ray light from linear to circular polarization, in practice such optics are challenging to fabricate and have poor throughput and limited bandwidth (3). A more appealing option is the direct generation of elliptically polarized (4-6) and circularly polarized (7-9) high harmonics. In recent work we showed that by using a combination of 0.8 and 0.4 μm counterrotating driving fields, bright (i.e., phase-matched) EUV HHG with circular polarization can be generated at wavelengths λ > 18 nm and used for EUV magnetic dichroism measurements (10-13).Here we make, to our knowledge, the first experimental demonstration of circularly polarized harmonics in the soft X-ray region to wavelengths λ < 8 nm, and use them to implement soft X-ray magnetic circular dichroism (XMCD) measurements using a tabletop-scale setup. By using counterrotating driving lasers at 0.79 μm (1.57 eV) and 1.3 μm (0.95 eV), we generate bright circularly polarized soft X-ray HHG beams with photon energies greater than 160 eV (14) and with flux comparable...

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High harmonic light sources make it possible to access attosecond timescales, thus opening up the prospect of manipulating electronic wave packets for steering molecular dynamics. However, two decades after the birth of attosecond physics, the concept of attosecond chemistry has not yet been realized; this is because excitation and manipulation of molecular orbitals requires precisely controlled attosecond waveforms in the deep UV, which have not yet been synthesized. Here, we present a unique approach using attosecond vacuum UV pulse-trains to coherently excite and control the outcome of a simple chemical reaction in a deuterium molecule in a non-Born-Oppenheimer regime. By controlling the interfering pathways of electron wave packets in the excited neutral and singly ionized molecule, we unambiguously show that we can switch the excited electronic state on attosecond timescales, coherently guide the nuclear wave packets to dictate the way a neutral molecule vibrates, and steer and manipulate the ionization and dissociation channels. Furthermore, through advanced theory, we succeed in rigorously modeling multiscale electron and nuclear quantum control in a molecule. The observed richness and complexity of the dynamics, even in this very simplest of molecules, is both remarkable and daunting, and presents intriguing new possibilities for bridging the gap between attosecond physics and attochemistry.chemical dynamics | electron dynamics | ultrafast T he coherent manipulation of quantum systems on their natural timescales, as a means to control the evolution of a system, is an important goal for a broad range of science and technology, including chemical dynamics and quantum information science. In molecules, these timescales span from attosecond timescales characteristic of electronic dynamics, to femtosecond timescales characteristic of vibrations and dissociation, to picosecond timescales characteristic of rotations in molecules. With the advent of femtosecond lasers, observing the transition state in a chemical reaction (1), and controlling the reaction itself, became feasible. Precisely timed femtosecond pulse sequences can be used to selectively excite vibrations in a molecule, allow it to evolve, and finally excite or deexcite it into an electronic state not directly accessible from the ground state (2). Alternatively, interferences between different quantum pathways that end up in the same final state can be used to control the outcome of a chemical reaction (3)(4)(5)(6)(7)(8)(9).In recent years, coherent high harmonic sources with bandwidths sufficient to generate either attosecond pulse trains or a single isolated attosecond pulses have been developed that are also perfectly synchronized to the driving femtosecond laser (10-12). This new capability provides intriguing possibilities for coherently and simultaneously controlling both the electronic and nuclear dynamics in a molecule in regimes where the BornOppenheimer approximation is no longer valid, to select specific reaction pathways or products. Here...