Laser-Induced Electron Diffraction for Probing Rare Gas Atoms

Recently, using midinfrared laser-induced electron diffraction (LIED), snapshots of a vibrating diatomic molecule on a femtosecond time scale have been captured [C. I. Blaga et al., Nature (London) 483, 194 (2012)]. In this Letter, a comprehensive treatment for the atomic LIED response is reported, a critical step in generalizing this imaging method. Electron-ion differential cross sections (DCSs) of rare gas atoms are extracted from measured angular-resolved, high-energy electron momentum distributions generated by intense midinfrared lasers. Following strong-field ionization, the high-energy electrons result from elastic rescattering of a field-driven wave packet with the parent ion. For recollision energies $\ge 100\mathrm{eV}$, the measured DCSs are indistinguishable for the neutral atoms and ions, illustrating the close collision nature of this interaction. The extracted DCSs are found to be independent of laser parameters, in agreement with theory. This study establishes the key ingredients for applying LIED to femtosecond molecular imaging.

Figure 1

(a) Extracted DCSs of Ar at 100 eV from HATI spectra for different combinations of laser intensities and wavelengths. Red empty circles: $2\mu \mathrm{m}$ and $235\mathrm{TW}/{\mathrm{cm}}^2$; magenta triangles: $2\mu \mathrm{m}$ and $200\mathrm{TW}/{\mathrm{cm}}^2$; cyan solid squares: $2.3\mu \mathrm{m}$ and $380\mathrm{TW}/{\mathrm{cm}}^2$. The corresponding ${\mathrm{U}}_p$ are 88 eV, 75 eV and 188 eV, respectively. Green filled circles are experimental DCSs for the $e$-Ar collision using electron guns [25], and the blue full curve are theoretical $e\mathrm{\text{−}}{\mathrm{Ar}}^{+}$ DCSs. (b) At 150 eV, $e\mathrm{\text{−}}{\mathrm{Ar}}^{+}$ DCS (red empty circles) is extracted from HATI spectra at $2\mu \mathrm{m}$ and $235\mathrm{TW}/{\mathrm{cm}}^2$, in comparison to the theoretical $e\mathrm{\text{−}}{\mathrm{Ar}}^{+}$ DCS (blue solid line) and experimental $e$-Ar DCS (green filled circles) [25]. (c) Same as (b) but for 200 eV. In (b), the theoretical DCS for an $e$-neutral collision [30] at 150 eV is also depicted by the magenta dashed line, in comparison to both the experimental and theoretical $e$-ion DCSs. The cyan dotted line in (b) is the DCS calculated using the atomic potential retrieved from an experimental $e$-ion DCS at 150 eV, see text.

Figure 2

Comparison of DCSs from LIED for Kr and Xe at 150 and 50 eV, respectively. DCS from HATI: red empty circles; theoretical $e$-ion: blue solid lines; experimental $e$-neutral: green filled circles [26, 27]; theoretical $e$-neutral: magenta dashed lines. DCSs calculated from these fitted potentials are also shown by the cyan dotted lines.

Figure 3

Retrieved atomic potentials with DCS from the LIED data in Fig. 1b, 2 for (a) Ar, (b) Kr, and (c) Xe, respectively. Cyan dotted lines are the fitted effective charges as a function of $r$, compared to a “known” potential for each atom (blue solid lines).

Figure 4

Returning electron wave packets against returning electron momentum extracted from the photoelectron spectra for different laser parameters and different atoms. (Target, wavelength in $\mu \mathrm{m}$, intensity in $\mathrm{TW}/{\mathrm{cm}}^2$) are: red filled circles: (Ar, 1.7, 208); green solid squares: (Ar, 2.0, 200); blue crosses: (Ar, 2.0, 215); purple asterisks: (Ar, 2.0, 235); magenta pluses: (Ar, 2.3, 380); orange solid inverted triangles: (Kr, 2.0, 180); maroon solid right triangles: (Kr, 2.3, 98); cyan solid diamonds: (Xe, 2.0, 72).