Proposal for Measuring Electron Displacement Induced by a Short Laser Pulse

In laser-matter interaction, most previous studies have focused on the change of the electron momentum induced by the external fields. Here, we theoretically investigate the electron displacement induced by an ultrashort pulse, whose precise waveform is hard to determine experimentally. We propose and numerically demonstrate a scheme to accurately measure the electron displacement using a ruler formed by the interfering spirals in the photoelectron momentum distribution generated by two oppositely circularly polarized pulses. The scheme is robust against the focusing volume effects and the jitter of the carrier envelope phase of the two circular pulses. The ability to measure the electron displacement by an arbitrary pulse may pave the way to quantitative control of the charge migration in matter on the scale of Ångström.

Figure 1

(a) The proposed configuration of laser pulses in a practical experimental measurement. From a numerical solution to the 3D TDSE, we get (b) the photoelectron distribution (PED) in the laser polarization plane, (c) the photoelectron angular distribution (PAD) at $p=0.35\mathrm{a}.\mathrm{u}.$, and (d) the angular stripe spacing (ASS) extracted from (c). The red solid curve in (d) is the analytical result from Eq. (4).

Figure 2

(a) Two oppositely circularly polarized pulses used to demonstrate the proposed scheme of measurement. (b) The ASS extracted for the ATI ring at $p=0.4$ from the TDSE, compared with the analytical result from Eq. (3). In (c), we illustrate the trajectory of the electron ionized at time $t_i=0$. Note the transversal displacement $r_{\perp }$ at the end of the pulse. The electron trajectory can also be plotted in the final momentum reference frame, as shown in (d), where $\mathbf{p}$ is the final momentum.

Figure 3

In (a), the same PADs as in Fig. 1 are, respectively, shown after averaging over the focusing volume effects (solid curve) and the jitter of CEP (dashed curve). From the averaged PAD from (a), the extracted ASS is shown in (b) (symbols) together with the analytical result (red solid line).