Tunneling Dynamics in Multiphoton Ionization and Attoclock Calibration

The intermediate domain of strong-field ionization between the tunneling and multiphoton regimes is investigated using the strong-field approximation and the imaginary-time method. An intuitive model for the dynamics is developed which describes the ionization process within a nonadiabatic tunneling picture with a coordinate dependent electron energy during the under-the-barrier motion. The nonadiabatic effects in the elliptically polarized laser field induce a transversal momentum shift of the tunneled electron wave packet at the tunnel exit and a delayed appearance in the continuum as well as a shift of the tunneling exit towards the ionic core. The latter significantly modifies the Coulomb focusing during the electron excursion in the laser field after exiting the ionization tunnel. We show that nonadiabatic effects are especially large when the Coulomb field of the ionic core is taken into account during the under-the-barrier motion. The simple man model modified with these nonadiabatic corrections provides an intuitive background for exact theories and has direct implications for the calibration of the attoclock technique.

Figure 1

The tunneling barrier of ionization in the case of a short-range atomic potential (solid, green line). The electron energy during the under-the-barrier motion: the nonadiabatic (short-dashed, blue line) and adiabatic (quasistatic) pictures (long-dashed, black line) in a (a) linearly or (b) circularly polarized laser field. The horizontal channel (tunneling) and the vertical channel (multiphoton ionization) are shown schematically by dashed green arrows. The interpretation of nonadiabatic tunneling as absorption of photons followed by tunneling with higher energy is shown with the (dot-dashed, red arrows) pathway in (a).

Figure 2

Ionization in a laser field with ellipticity of $\epsilon =0.87$. (a) The asymptotic momentum distribution and the corresponding quasistatic result are shown as a dashed ellipse for $\gamma =1$. (b) The exit coordinate vs the Keldysh parameter. (c) The most probable transverse momentum at the tunneling exit $p_{\perp e}$ vs the Keldysh parameter. (d) The complex time contour during tunneling in the Coulomb potential (the red, solid line) and the zero-range potential (black, dashed line) for $E_0=0.1\mathrm{a}.\mathrm{u}.$ (the arrows show the integration direction). (e) The nonadiabatic time delay $t_e$ vs the Keldysh parameter at $E_0=0.02\mathrm{a}.\mathrm{u}.$ (f) The emission angle of the most probable photoelectrons vs the Keldysh parameter. In (b), (c), and (f) the nonadiabatic case for the Coulomb potential (the red, solid line), the quasistatic case in the Coulomb potential (the black, long-dashed line), and the nonadiabatic case in the zero-range potential (the blue, short-dashed line) are plotted. In (f) only the nonadiabatic momentum shift at the tunnel exit (the green, dot-dashed line) is taken into account in the otherwise quasistatic case of a zero-range potential, and experimental data of Ref. [6] are displayed as black dots.