Attosecond Imaging of Electronic Wave Packets

An electronic wave packet has significant spatial evolution besides its temporal evolution, due to the delocalized nature of composing electronic states. The spatial evolution was not previously accessible to experimental investigations at the attosecond timescale. A phase-resolved two-electron-angular-streaking method is developed to image the shape of the hole density of an ultrafast spin-orbit wave packet in the krypton cation. Furthermore, the motion of an even faster wave packet in the xenon cation is captured for the first time: An electronic hole is refilled 1.2 fs after it is produced, and the hole filling is observed on the opposite side where the hole is born.

Figure 1

Attosecond imaging of electronic wave packets. (a) Top: the temporal evolution of electronic wave packets in the form of hole density in the xenon cation (left) and krypton cation (right). Bottom: the calculated time- and angle-dependent ionization rates of an electronic wave packet with an initial phase of 0°. The angle dependence arises from the shape of hole density. The yellow lines represent the rotating electric field probing at different directions and time delays. The inset between the two plots illustrates how the rotating electric field of circularly polarized light can map the shape of electron (hole) density. (b) The experimental setup for achieving phase-resolved $2e\mathrm{AS}$.

Figure 2

(a) Calculated time transients of second ionization yields of electronic wave packets in xenon and krypton cations as probed by a circularly polarized strong field, i.e., the ionization yields integrated along the yellow diagonal lines in Fig. 1. Both were normalized to their corresponding maxima. (b) Experimentally obtained time transients of double ionization yields in xenon (red) and krypton (blue). The curves are the cubic spline fittings of the data points (blue round for krypton and red square for xenon). They were both normalized to their own maxima. The black curve and data points show the result of false coincidence events (two electrons plus a single cation), suggesting the system bias is minimal even with a high false coincidence rate. $x\text{−}y$ plane is the plane of polarization.

Figure 3

Resolving the direction of time in $2e\mathrm{AS}$ with absolute CEP measurements in (a) xenon and (b) krypton. Comparison between time transients obtained with employing momentum magnitude or absolute CEP as the discriminators.

Figure 4

Fully corrected time transients showing the time-resolved double ionization yields reflecting the spatiotemporal evolution of electronic wave packets in (a) xenon and (b) krypton. The insets show the time-dependent functions used to correct the enveloped induced first ionization bias. The curves are the inverse of the sum between ionization probabilities of neutral xenon and krypton and time-independent background signals arising from false coincidence events.