Quantitative rescattering theory for nonsequential double ionization of atoms by intense laser pulses

Laser-induced electron recollisions are fundamental to many strong field phenomena in atoms and molecules. Using the recently developed quantitative rescattering theory, we demonstrate that the nonsequential double ionization (NSDI) of atoms by lasers can be obtained quantitatively in terms of inelastic collisions of the target ions with the free returning electrons where the latter are explicitly given by a spectrum-characterized wave packet. Using argon atoms as target, we calculated the NSDI yield including contributions from direct $(e,2e)$ electron-impact ionization and electron-impact excitation accompanied by subsequent field ionization. We further investigate the dependence of total NSDI on the carrier-envelope phase of few-cycle laser pulses, and showed that the effect can be experimentally observed by measuring the yield of doubly charged ions only.

Figure 1

(Color online) Volume-integrated electron wave packets extracted from photoelectron spectra on the “right” side, for atomic argon singly ionized by a five-cycle laser pulse with a mean wavelength of $800\mathrm{nm}$, for CEP equals to zero, and different peak intensities (with $I_0=1.0\times {10}^{14}\mathrm{W}∕{\mathrm{cm}}^2$). The total electron-impact ionization and excitation cross sections from the ground state of ${\mathrm{Ar}}^{+}$ are also presented.

Figure 2

(Color online) Electron-impact ionization and excitation cross sections for the ground state of ${\mathrm{Ar}}^{+}$. The ionization cross section is calculated by means of the Lotz formula. The excitation cross sections (full line with various symbols) are determined from an empirical formula [44] adjusted to fit distorted-wave Born approximation calculations [45] at high-energy (dashed lines), see text.

Figure 3

(Color online) Nonsequential double ionization yield for argon atoms as a function of the peak intensity for a linearly polarized laser pulse with mean wavelength of $800\mathrm{nm}$. The red crosses are experimental results from Ref. 46 for a $30\mathrm{fs}$ pulse duration. The blue stars are from calculations when depletion effects and collisional ionization and excitation processes are considered. The results when depletion effects are omitted are shown as green circles, and the contribution when only direct ionization is included is represented by black squares.

Figure 4

(Color online) Left (a), right (b), and total (c) volume-integrated wave packets for argon atoms in a five-cycle laser pulse with a peak intensity of $2.0\times {10}^{14}\mathrm{W}∕{\mathrm{cm}}^2$, a mean wavelength of $800\mathrm{nm}$, and different carrier-envelope phases. The electron-impact inelastic cross section for the ground state of ${\mathrm{Ar}}^{+}$ is also shown. (d) Nonsequential double ionization yield as a function of the absolute phase of a five-cycle laser pulse with a mean wavelength of $800\mathrm{nm}$ and different peak intensities.