Imaging Density Disturbances in Water with a 41.3-Attosecond Time Resolution

Abstract

We show that the momentum flexibility of inelastic x-ray scattering may be exploited to invert its loss function, alowing real time imaging of density disturbances in a medium. We show the disturbance arising from a point source in liquid water, with a resolution of 41.3 attoseconds (4.13 × 10 −17 sec) and 1.27Å (1.27×10 −8 cm). This result is used to determine the structure of the electron cloud around a photoexcited chromophore in solution, as well as the wake generated in water by a 9 MeV gold ion. We draw an analogy with pump-probe techniques and suggest that energy-loss scattering may be applied more generally to the study of attosecond phenomena.Brisk progress has been made recently in the generation and detection of ultrashort, attosecond (1 as = 10 −18 sec) laser pulses with high harmonic generation techniques [1, 2,3,4,5,6,7,8]. This has heralded an age of attophysics in which many-electron dynamics will be probed in real time. Much of what is already known about electron dynamics has been derived from energy-loss techniques such as inelastic x-ray, electron, or neutron scattering, which have been fruitfully applied to the study of, for example, plasma oscillations, exciton dynamics, and spin waves. Such experiments are normally examined in the frequency / momentum representation, where the spectra may be easily compared to theoretically calculable response functions for the electron density or local magnetic moment. However if such measurements truly reflect dynamics, a temporal representation may also be illuminating.In this letter we demonstrate a method for inverting energy-loss measurements into time and space, permitting explicit imaging of electron dynamics in a medium. This allows the spatial extent of excited states to be determined, i.e. the mean free path or dephasing distance, and a parallel with pump-probe techniques to be drawn. Inverting requires reliable sampling of a loss function along both energy and momentum axes with sufficient range to resolve the features of interest and sufficient resolution to provide an adequate field of view. Therefore, because of its kinematic flexibility, we consider the case of inelastic x-ray scattering (IXS).In IXS a photon with well-defined initial momentum and energy, (k i , ω i ), is impinged on a specimin which scatters it to a final (k f , ω f ). The spectral density of scattered photons is proportional to the dynamic structure factor of the material, S(k, ω), where ω = ω i − ω f and k = k i −k f are the transferred energy and momentum [9]. S(k, ω) was posed originally by van Hove[10] as a measure of the dynamical properties of an interacting electron system, and by the fluctuation-dissipation theorem is related to the imaginary part of a response function[11]which can thereby be experimentally determined. χ(k, ω)is known as the density Green's function, or density propagator, and describes the way disturbances in the electron density propagate in the system. χ(k, ω) is the space-time fourier transform of χ(x, t) = −i < 0|[δn(x, t), δn(0, 0)]|0 > θ(t...

Dynamics of confined water reconstructed from inelastic x-ray scattering measurements of bulk response functions

“…This technique has been used to study a broad range of systems [27,28]. The recent development of Green's function imaging (GFI) [21,29,30] combined with high-intensity third generation synchrotron sources have allowed ultrafast movies at subangstrom spatial resolution to be made. In our IXS experiment [ Fig.…”

Crystallographic refinement of collective excitations using standing wave inelastic X-ray scattering

“…[6,4] If successfully implemented, this approach would reveal the complete density response, χ(x 1 , x 2 , t), which describes the electron disturbance created by a source placed at any arbitrary location, Analyzing a simple model of a single quantum particle in a periodic potential, we have shown that standing wave IXS imaging is an innately three-dimensional measurement, in the sense that both out-of-plane analyzer motions and sample Ψ-rotations are required to achieve a complete data set. Such an experiment would require (at the minimum) two copies of the crystal of interest: one that is asymmetrically cut to collimate the beam, and a second to create the standing wave field and function as the "sample".…”

“…[4] However, it provides explicit, real-space images, and contains no intrinsic limit on the achievable time resolution: attosecond or even zeptosecond resolution is achievable. So far, IXS imaging has been used to study collective electron dynamics in liquid water, [6,7] excitons in large-gap insulators, [8] and to measure the effective fine structure constant of graphene. [9] Up to now, however, there has been a limitation on the imaging aspect of this approach.…”

“…We begin by reviewing spatially-averaged IXS imaging, as it has been implemented previously [6,8,9] (for a more thorough review, see ref. [4]).…”

Imaging instantaneous electron flow with ultrafast resonant x-ray scattering

“…In a time-resolved measurement, where the pulse duration must be much shorter than the characteristic time of the electron dynamics, the incoming photon energy is not precisely defined, and the signal depends on the spectrum of the broadband probe pulse [36]. Spectrally resolved inelastic x-ray scattering from a stationary system encodes a dynamic structure factor, which can provide access to electron dynamics at the level of linear response theory [41,42]. Our method measures the state of an electron system at a given time independently from how this state had been created.…”