Phase-dependent atomic ionization in few-cycle intense laser fields

We have studied the carrier-envelope phase-dependent above-threshold-ionization processes by solving the time-dependent Schrödinger equation nonperturbatively. Our simulated carrier-envelope phase-dependent above-threshold-ionization spectra are in good agreement with the experimental measurement of Paulus et al. [Phys. Rev. Lett. 91, 253004 (2003)] if we shift the experimental carrier-envelope phase by $0.15\pi$. This means that we have recalibrated the carrier-envelope phase more accurately by comparing our simulations with the experimental measurements. Furthermore, by tracing back the origin of the ionized electrons, we have clearly identified that the low-energy electrons come from the direct ionization by the laser field and the high-energy electrons come from the recollision with the parent core after being bounced back by the laser field.

Figure 1

(Color online) Ionization yields to the right and left sides as a function of the CE phase. The laser intensity is $6\times {10}^{13}\mathrm{W}∕{\mathrm{cm}}^2$ and laser pulse duration is $6\mathrm{fs}$ with central wavelength of $800\mathrm{nm}$.

Figure 2

(Color online) Ratio of the ionization yields from the right and left sides for different photoelectron energies as a function of the CE phase. The laser parameters are the same as ones used in Fig. 1. The solid triangles are the original experimental data [22]. The experimental CE phase shifted by $0.15\pi$ is also plotted (solid circles).

Figure 3

(Color online) Simulated electron energy spectra from the right (right panel) and left (left panel) sides in the ultrashort intense laser field for $\delta =0$. The time-dependent laser field is depicted in the middle panel. The straight arrows stand for the direct ionization and the curved arrows stand for the scattering part. $A_{-1}$ and $B_0$ stand for the spectra without the ionization contribution from peak $A_{-1}$ or $B_0$. The laser parameters are the same as the ones used in Fig. 1.