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

We show that the momentum flexibility of inelastic x-ray scattering may be exploited to invert its loss function, allowing 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 ($4.13\times {10}^{-17}\mathrm{s}$) and $1.27\AA$ ($1.27\times {10}^{-8}\mathrm{cm}$). 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.

Figure 1

False color plot of $-\mathrm{Im}[\chi (\mathbf{k},\omega )]$ for water in units of $\mathrm{as}/{\AA }^3$, plotted against transferred momentum (horizontal axis, in ${\AA }^{-1}$) and energy (vertical axis, in eV). The broad feature is the valence plasmon, corresponding to collective oscillation of the $2s$ and $2p$ shells of oxygen.

Figure 2

Individual spectra at $k=0.583{\AA }^{-1}$ (above) and $k=4.95{\AA }^{-1}$ (below), showing the raw data (open circles), extrapolated tails (red lines), and the resulting real part (green) line.

Figure 3

Time frames of $\chi (\mathbf{x},t)$ derived from Fig. 1, in units of ${\AA }^{-6}$. The vertical scale has been clipped at $1{\AA }^{-6}$ in frames (a)–(g), $0.1{\AA }^{-6}$ in (h), and $0.005{\AA }^{-6}$ in (i). Distances are indicated with scale bars. (a) At $t<0$, before the perturbation, the system is “placid.” (b) Shortly after the impulse, showing a large (off scale) negative recoil at $|x|=0$ surrounded by compensating positive buildup. (c)–(g) Evolution of this disturbance at selected later times. (h) Same as (b) but on an expanded scale, showing distant Friedel-like oscillations. (i) After the disturbance has damped, scale expanded to show the experimental noise level.

Figure 4

Electron density disturbances for two extended sources, constructed via Eq. (4). (a) Induced charge around an oscillating dipole, such as a photoexcited chromophore in solution, at the peak of its cycle and (b) the wake produced in water by a 9 MeV gold ion. The ion location and direction of motion are indicated by the red arrow.