Nonsequential double ionization with time-dependent renormalized-natural-orbital theory

Recently introduced time-dependent renormalized-natural-orbital theory (TDRNOT) is tested on nonsequential double ionization (NSDI) of a numerically exactly solvable one-dimensional model He atom subject to few-cycle, 800-nm laser pulses. NSDI of atoms in strong laser fields is a prime example of nonperturbative, highly correlated electron dynamics. As such, NSDI is an important “worst-case” benchmark for any time-dependent few and many-body technique beyond linear response. It is found that TDRNOT reproduces the celebrated NSDI “knee,” i.e., a many-order-of-magnitude enhancement of the double-ionization yield (as compared to purely sequential ionization) with only the ten most significant natural orbitals (NOs) per spin. Correlated photoelectron spectra—as “more differential” observables—require more NOs.

Figure 1

Double-ionization probability vs laser intensity. TDRNOT results with $N=1,2,3,4,6,10$ spatial RNOs (red, +) are compared with the exact TDSE result (black, dots) and with the ionization probability reconstructed using the first $N$ exact NOs calculated from the exact TDSE wave function (green, $\times )$.

Figure 2

TDSE-benchmark two-electron photoelectron spectrum ${\rho }^{2+}\left(p_1{p}_2\right)$ at $I=2.25\times {10}^{15}\mathrm{W}/{\mathrm{cm}}^2$.

Figure 3

${\rho }^{2+}\left(p_1{p}_2\right)$ at $I=2.25\times {10}^{15}\mathrm{W}/{\mathrm{cm}}^2$ obtained from the $N=1,2,5,6,10,15$ dominant, exact spatial NOs calculated from the exact TDSE wave function after the laser pulse.

Figure 4

${\rho }^{2+}\left(p_1{p}_2\right)$ at $I=2.25\times {10}^{15}\mathrm{W}/{\mathrm{cm}}^2$ obtained from TDRNOT with $N=1,2,5,6,10,15$ spatial RNOs.

Figure 5

${\rho }^{2+}\left(p_1{p}_2\right)$ at $I=2.25\times {10}^{15}\mathrm{W}/{\mathrm{cm}}^2$ obtained from TDRNOT with $N=15$ spatial RNOs propagated but only $N=5$ and 6 used to calculate ${\rho }^{2+}\left(p_1{p}_2\right)$.