Adiabaticity in the lateral electron-momentum distribution after strong-field ionization

By solving the time-dependent Schrödinger equation for atoms in short laser pulses of different polarizations, it is shown that in strong-field ionization without rescattering, the lateral width of the electron-momentum distribution corresponds adiabatically to the instantaneous laser field on a sub-laser-cycle time scale, as expected in pure tunneling ionization. In contrast to the distributions along the polarization direction, the width is affected little by depletion or Coulomb effects.

Figure 1

(a) Longitudinal momentum distribution $P^{\mathrm{LP}}\left(k_z\right)$ at $E_0=0.12$ a.u. and (b) angular distribution $P^{\mathrm{CP}}\left(\varphi \right)$ at $E_0=0.027$ a.u. from the TDSE and the two semiclassical SM and CC models.

Figure 2

Momentum distribution from three-cycle CP pulses, integrated along $k_z$ into the $xy$ plane of polarization at (a) $E_0=$ 0.046 a.u. and (b) $E_0=$ 0.084 a.u. The dotted curves show the predictions of the SM model, while the solid black curve in (b) indicates the lower integration limit $k_i$ for Eq. (6).

Figure 3

(a) Width ${\sigma }^{\mathrm{LP}}\left(k_z\right)$ obtained at $E_0=0.2$a.u. from the TDSE, the exact adiabatic model, and the tunneling model. (b) Width ${\sigma }^{\mathrm{CP}}\left(\varphi \right)$ obtained at $E_0=0.027$a.u. from the TDSE and the tunneling model. Also shown are the corresponding TDSE longitudinal and angular distributions $P^{\mathrm{LP}}\left(k_z\right)$ and $P^{\mathrm{CP}}\left(\varphi \right)$, respectively (not to scale). Tunneling model refers to the tunneling product formula [Eq. (9)] combined with the SM model.

Figure 4

Position of the maximum in the (a) longitudinal distribution $P^{\mathrm{LP}}\left(k_z\right)$ and (b) lateral width ${\sigma }^{\mathrm{LP}}\left(k_z\right)$, plotted versus field amplitude for the LP pulse.

Figure 5

Positions of maxima in the (a) angular distribution $P^{\mathrm{CP}}\left(\varphi \right)$ and (b) width ${\sigma }^{\mathrm{CP}}\left(\varphi \right)$, plotted versus field amplitude for the CP pulse. The vertical line in (b) is due to trajectories that do not escape the core potential.

Figure 6

(a) Maximum widths ${\sigma }_{\max }^{\mathrm{LP}}\left(E_0\right)$ from the TDSE, from the tunneling product formula, and from the exact adiabatic model versus field amplitude $E_0$. Also shown is the width at the maximum of the longitudinal distribution. Shown on the right is the width ${\sigma }^{\mathrm{LP}}\left(k_z\right)$ versus longitudinal momentum for (b) 1600 nm and $E_0=$ 0.10 a.u., (c) 800 nm and $E_0=$ 0.12 a.u., and (d) 400 nm and $E_0=$ 0.14 a.u. The total ionization probability was approximately 0.5 in each case.