Long-range Coulomb effect in above-threshold ionization of Ne subject to few-cycle and multicycle laser fields

The long-range Coulomb effect (LRCE) is demonstrated experimentally and theoretically by investigating the pulse duration dependence of low-energy structure (LES) in above-threshold ionization of Ne. It is found experimentally that at 800 nm the LES shows itself as a double-hump structure (DHS) in momentum distribution of singly charged ion for Ne, and moreover, this structure is more prominent for multicycle laser fields than for few-cycle cases. This result can be reproduced and explained qualitatively with a semiclassical model and attributed to the paramount role of LRCE. That is to say, after the laser field vanishes, the electrons decelerate while flying away from the core by the long-range tail of Coulomb potential, which eventually makes DHS less notable.

Figure 1

The measured [(a), (c), (e)] and calculated [(b), (d), (f)] longitudinal momentum distributions (LMDs) integrated over the transverse momentum of ${\mathrm{Ne}}^{+}$ for the pulse durations of 7 fs (thick black line) and 30 fs (thin red line). The laser intensities are $5.0\times {10}^{14}{\mathrm{W}/\mathrm{cm}}^2$ for panels (a) and (b), $3.8\times {10}^{14}{\mathrm{W}/\mathrm{cm}}^2$ for panels (c) and (d), and $2.9\times {10}^{14}{\mathrm{W}/\mathrm{cm}}^2$ for panels (e) and (f).

Figure 2

Calculated momentum distributions for two pulse durations with different evolutionary times: (a) $t_{\mathrm{final}}=t_{\mathrm{zero}}$, (c) $t_{\mathrm{final}}=100T$. (b) The ionization yields with respect to the strength of the Coulomb potential at $t_{\mathrm{final}}=t_{\mathrm{zero}}$. (d) The ionization yields with respect to the distance between the photoelectron and the center of the Coulomb potential at $t_{\mathrm{final}}=t_{\mathrm{zero}}$. The intensity is $5.0\times {10}^{14}{\mathrm{W}/\mathrm{cm}}^2$.

Figure 3

Calculated $p_z$ vs time for two well-chosen orbits in the laser field with pulse duration of 7 fs. Right after the laser field ends (as indicated by the black vertical arrow), the momenta for both orbits are 0.14 a.u. Thereafter, the two orbits evolve differently due to the LRCE. Inset (a) shows $p_z$ evolution vs time for the two orbits in a longer time interval for pulse duration of 7 fs. Inset (b) is the same as inset (a) except for the pulse duration of 30 fs. Inset (c) shows the distances between the ionized electron and the core vs time for orbit 1 for the two pulse durations. Inset (d) shows the corresponding results for orbit 2. The thick and thin blue vertical lines in insets (c) and (d) indicate the moment when the laser pulse vanishes for the pulse durations of 7 and 30 fs, respectively.