The superposition of quantum states drives motion on the atomic and subatomic scales, with the energy spacing of the states dictating the speed of the motion. In the case of electrons residing in the outer (valence) shells of atoms and molecules which are separated by electronvolt energies, this means that valence electron motion occurs on a subfemtosecond to few-femtosecond timescale (1 fs = 10(-15) s). In the absence of complete measurements, the motion can be characterized in terms of a complex quantity, the density matrix. Here we report an attosecond pump-probe measurement of the density matrix of valence electrons in atomic krypton ions. We generate the ions with a controlled few-cycle laser field and then probe them through the spectrally resolved absorption of an attosecond extreme-ultraviolet pulse, which allows us to observe in real time the subfemtosecond motion of valence electrons over a multifemtosecond time span. We are able to completely characterize the quantum mechanical electron motion and determine its degree of coherence in the specimen of the ensemble. Although the present study uses a simple, prototypical open system, attosecond transient absorption spectroscopy should be applicable to molecules and solid-state materials to reveal the elementary electron motions that control physical, chemical and biological properties and processes.

An era of exploring the interactions of high-intensity, hard X-rays with matter has begun with the start-up of a hard-X-ray free-electron laser, the Linac Coherent Light Source (LCLS). Understanding how electrons in matter respond to ultra-intense X-ray radiation is essential for all applications. Here we reveal the nature of the electronic response in a free atom to unprecedented high-intensity, short-wavelength, high-fluence radiation (respectively 10(18) W cm(-2), 1.5-0.6 nm, approximately 10(5) X-ray photons per A(2)). At this fluence, the neon target inevitably changes during the course of a single femtosecond-duration X-ray pulse-by sequentially ejecting electrons-to produce fully-stripped neon through absorption of six photons. Rapid photoejection of inner-shell electrons produces 'hollow' atoms and an intensity-induced X-ray transparency. Such transparency, due to the presence of inner-shell vacancies, can be induced in all atomic, molecular and condensed matter systems at high intensity. Quantitative comparison with theory allows us to extract LCLS fluence and pulse duration. Our successful modelling of X-ray/atom interactions using a straightforward rate equation approach augurs favourably for extension to complex systems.

Manipulation of electron dynamics calls for electromagnetic forces that can be confined to and controlled over sub-femtosecond time intervals. Tailored transients of light fields can provide these forces. We report on the generation of subcycle field transients spanning the infrared, visible, and ultraviolet frequency regimes with a 1.5-octave three-channel optical field synthesizer and their attosecond sampling. To demonstrate applicability, we field-ionized krypton atoms within a single wave crest and launched a valence-shell electron wavepacket with a well-defined initial phase. Half-cycle field excitation and attosecond probing revealed fine details of atomic-scale electron motion, such as the instantaneous rate of tunneling, the initial charge distribution of a valence-shell wavepacket, the attosecond dynamic shift (instantaneous ac Stark shift) of its energy levels, and its few-femtosecond coherent oscillations.

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We present an implementation of the time-dependent configuration-interaction singles (TDCIS) method for treating atomic strong-field processes. In order to absorb the photoelectron wave packet when it reaches the end of the spatial grid, we add to the exact nonrelativistic many-electron Hamiltonian a radial complex absorbing potential (CAP). We determine the orbitals for the TDCIS calculation by diagonalizing the sum of the Fock operator and the CAP using a flexible pseudospectral grid for the radial degree of freedom and spherical harmonics for the angular degrees of freedom. The CAP is chosen such that the occupied orbitals in the Hartree-Fock ground state remain unaffected. Within TDCIS, the many-electron wave packet is expanded in terms of the Hartree-Fock ground state and its single excitations. The virtual orbitals satisfy nonstandard orthogonality relations, which must be taken into consideration in the calculation of the dipole and Coulomb matrix elements required for the TDCIS equations of motion. We employ a stable propagation scheme derived by second-order finite differencing of the TDCIS equations of motion in the interaction picture and subsequent transformation to the Schrödinger picture. Using the TDCIS wave packet, we calculate the expectation value of the dipole acceleration and the reduced density matrix of the residual ion. The technique implemented will allow one to study electronic channel-coupling effects in strong-field processes.

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Imaging the quantum motion of electrons not only in real-time, but also in real-space is essential to understand for example bond breaking and formation in molecules, and charge migration in peptides and biological systems. Time-resolved imaging interrogates the unfolding electronic motion in such systems. We find that scattering patterns, obtained by X-ray time-resolved imaging from an electronic wavepacket, encode spatial and temporal correlations that deviate substantially from the common notion of the instantaneous electronic density as the key quantity being probed. Surprisingly, the patterns provide an unusually visual manifestation of the quantum nature of light. This quantum nature becomes central only for non-stationary electronic states and has profound consequences for time-resolved imaging.X-ray imaging | attosecond science | quantum electrodynamics T he scattering of light from matter is a fundamental phenomenon that is widely applied to gain insight about the structure of materials, biomolecules and nanostructures. The wavelength of X-rays is of the order of atomic distances in liquids and solids, which makes X-rays a very convenient probe for obtaining realspace, atomic-scale structural information of complex materials, ranging from molecules (1) to proteins (2) and viruses (3). The power of X-ray scattering relies as well on the fact that the X-rays interact very weakly with the electrons in matter. In a given macroscopic sample, generally no more than one scattering event per X-ray photon takes place, the probability for multiple scattering being extremely small. The key quantity in X-ray scattering is the differential scattering probability (DSP), which is related to the Fourier transform of the electronic density ρðxÞ as follows (4, 5)where dP e ∕dΩ is the differential scattering probability from a free electron and Q is proportional to the momentum transfer of the scattered light. Procedures exist, for both crystalline (6) and non-crystalline samples (7), to reconstruct ρðxÞ from the scattering pattern. Equation 1 can be obtained from a purely classical description of electromagnetic radiation scattered by a stationary electron density (5), yielding a result identical to that obtained from a quantum electrodynamics (QED) description of light. Eq. 1 gives us access to a static view of the electronic density. On the other hand, much progress has been made in recent years towards understanding electronic motion with time-domain table-top experiments (8-13), owing to the availability of laser pulses on the sub-fs time scale (14,15). An ultimate goal of imaging applications encompasses unraveling the motion of electrons and atoms with spatial and temporal resolutions of order 1 Å and 1 fs, respectively (16). Recent breakthroughs make it possible to generate hard X-ray pulses of a few fs (17, 18), and pulses of length 100 as can in principle be realized (19,20). Hence, a fundamental question that needs to be addressed is: How does an ultrashort light pulse interact and scatter from a non-stationary...

X-ray free-electron lasers provide unique opportunities for exploring ultrafast dynamics and for imaging the structures of complex systems. Understanding the response of individual atoms to intense X-rays is essential for most free-electron laser applications. First experiments have shown that, for light atoms, the dominant interaction mechanism is ionization by sequential electron ejection, where the highest charge state produced is defined by the last ionic state that can be ionized with one photon. Here, we report an unprecedentedly high degree of ionization of xenon atoms by 1.5 keV free-electron laser pulses to charge states with ionization energies far exceeding the photon energy. Comparing ion charge-state distributions and fluorescence spectra with state-of-the-art calculations, we find that these surprisingly high charge states are created via excitation of transient resonances in highly charged ions, and predict resonance enhanced absorption to be a general phenomenon in the interaction of intense X-rays with systems containing high-Z constituents