Keldysh parameter, photoionization adiabaticity, and the tunneling time

Ultrafast photoionization dynamics within a driver field cycle is shown to be the key to understanding the multifaceted role of the Keldysh parameter γ as the borderline between multiphoton and tunneling ionization, ionization adiabaticity degree, and a measure for the electron tunneling time. We demonstrate that, when applied to subcycle ionization dynamics, the $\gamma \ll 1$ condition automatically translates into a criterion of both adiabaticity and photoionization via tunneling. We also show that the ratio of the Keldysh γ to the frequency of the driver field indeed defines an important time scale of photoionization. However, instead of connecting to the electron motion beneath the potential barrier, it relates to the time needed for an electron to acquire a pondermotive energy equal to the ionization potential. This time scale is shown to manifest itself in the experimentally measurable buildup time of the photoelectron yield.

Figure 1

Tunneling of an electron through the potential of an atomic nucleus (blue dashed line) modified by the electric field $E_0$ (the energy of interaction with this field is shown by the green dashed line). The wave function of the initial bound state of an electron is shown by the blue line. The wave function of a free electron in an ac electric field is shown by the red line. Tunneling via beneath-the-barrier passage is shown by the dashed arrow. The dial shows the imaginary time related to this process.

Figure 2

The thickness $z_0$ of the potential barrier formed by the potential of an atomic nucleus and a laser field with a field intensity of $500\mathrm{TW}/\mathrm{c}{\mathrm{m}}^2$ and a wavelength of 800 nm found as the solution of the $\mathrm{\Phi }\left(z,\theta \right)=0$ equation (red solid line) and using the approximate solution to this equation given by Eq. (12) (dash-dotted line). The green solid line shows the pondermotive energy $U_{\mathrm{p}}$ of the electron as a function of time θ, measured in field cycles. Also shown is the time ${\tau }_0$ required for an electron to gain the potential energy $U_{\mathrm{p}}$ equal to the ionization potential $I_0$ (shown by the horizontal dashed line).