Nonsequential Double Ionization as a Completely Classical Photoelectric Effect

We introduce a unified and simplified theory of atomic double ionization. Our results show that at high laser intensities ($I\ge {10}^{14}\mathrm{W}/{\mathrm{c}\mathrm{m}}^2$) purely classical correlation is strong enough to account for all of the main features observed in experiments to date.

Figure 1

Energy versus time plots showing four distinct stages of NSDI. The orange (fainter in gray scale) and blue (darker in gray scale) lines track the energies of two electrons. After repeated exchanges of energy while both are bound, one-electron (orange or fainter line) acquires positive energy but returns a number of times to the core. Its strong recollisions show up as spikes in the energy line of the still-bound inner electron. After several spikes the phasing is right to liberate the inner electron and the doubly ionized pair exhibit free-electron jitter motion.

Figure 2

Classical energy trajectories calculated in three dimensions. Here the same characteristic four stages of NSDI include two strong recollisions.

Figure 3

The “knee” signature of NSDI data (solid dots) is clearly predicted even in a classical calculation. The dashed curve (red) is inserted by hand to indicate the prediction made by sequential quantum tunneling theory [1].

Figure 4

Final ion momentum distributions of neon [6], helium [5], and argon [7] measured using COLTRIMS. Panels (b) and (d) show the momentum distribution of He ions at different laser intensities. Two solid curves (red) and a dashed curve (blue) are inserted by hand under the experimental data to identify contributions from the two types of NSDI trajectory. One type gives distributions peaked at zero (Z) momentum, and the other gives distributions with symmetrically placed nonzero (NZ) momentum peaks. The relative sizes of the Z and NZ peaks in each distribution depend on the atomic species and the laser intensities.

Figure 5

Final ion momentum distributions calculated classically at two laser intensities using the classical ensemble method as indicated by dots connected with a line. The letters Z and NZ label the peaks of the broad but distinct groups of trajectories (represented by a dashed curve and two solid curves as in Fig. 4) with small or zero ion momentum and substantially nonzero ion momentum, respectively.