Time-dependent density-functional theory of strong-field ionization of atoms by soft x rays

We demonstrate the capabilities of time-dependent density functional theory (TDDFT) for strong-field, short-wavelength (soft x-ray) physics, as compared to a formalism based on rate equations. We find that TDDFT provides a very good description of the total and individual ionization yields for Ne and Ar atoms exposed to strong laser pulses. We assess the reliability of different adiabatic density functionals and conclude that an accurate description of long-range interactions by the exchange and correlation potential is crucial for obtaining the correct ionization yield over a wide range of intensities (from ${10}^{13}$ to $5\times {10}^{15}{\mathrm{W}/\mathrm{cm}}^2$). Our TDDFT calculations disentangle the contribution from each ionization channel based on the Kohn-Sham wave functions.

Figure 1

Ne total number of escaped electrons $N_{\mathrm{esc}}$ for different laser intensities and (a) 5 fs and (b) 30 fs FWHM pulses of $\omega =93$ eV. Different TDDFT functionals are compared with LOPT. The Ne ionization process is shown as an inset. Shaded regions indicate the electrons frozen in the pseudopotential.

Figure 2

As in Fig. 1, but for a 5 fs FWHM pulse and different approximation levels: LB94, LDA, CXD-LDA, and PBE. In each panel we compare LOPT (solid), TDDFT (dashed), and the independent KS response (dotted). Shaded regions indicate the electrons included in the pseudopotential.

Figure 3

Ne individual ionization yields as a function of the intensity for 5 fs and 30 fs FWHM laser pulses of $\omega =93$ eV. TDDFT (thicker) and the independent KS response (thinner) with LB94 (dashed) and LDA (dotted) functionals are compared to LOPT (solid). The individual channels are sorted in increasing order from left to right according to their charge status.

Figure 4

Ar total and individual ionic yields as a function of the laser intensity for a 10 fs FWHM laser pulse of $\omega =105$ eV. (a) Total ionization yield for different TDDFT functionals and LOPT. (b) Individual ionization channels for LB94 (dashed) and LOPT (solid). The individual channels are sorted in increasing order from left to right according to their charge status. The Ar ionization process is shown as an inset. Shaded regions indicate electrons frozen in the pseudopotential.

Figure 5

Ne absorption cross section (logarithmic scale) above the first ionization threshold. Result for different TDDFT xc functionals (LDA, PBE, CXD-LDA, and LB94) compared with experimental data [43]. In the inset we focus on the range of energies relevant for ionization from a $\omega =93$ eV laser pulse.

Figure 6

Same as in Fig. 5, but for the Ar absorption cross section. In the inset we focus on the range of energies relevant for ionization from a $\omega =105$ eV laser pulse.