Probing Nonadiabatic Effects in Strong-Field Tunnel Ionization

We investigate experimentally the validity of proposed theories extending the tunneling approximation towards the multiphoton regime in strong-field ionization of helium. We employ elliptically polarized laser pulses and demonstrate how the influence of the ion potential on the released electron encoded in the measured observable provides the desired sensitivity to detect nonadiabatic effects in tunnel ionization. Our results show that for a large intensity range the proposed nonadiabatic theories contradict the experimental trends of the data, while adiabatic assumptions are confirmed.

Figure 1

(a) Potential energy surface of laser-induced ionization showing possible ionization mechanisms. (b),(c) Measured momentum distributions from strong-field ionization of helium with elliptically polarized pulses at an intensity of about $7\times {10}^{14}$ and $2\times {10}^{14}\mathrm{W}/{\mathrm{cm}}^2$ respectively, with an ellipticity of $\epsilon =0.87$. In (b), the orientation of the polarization ellipse, with its major axis along $p_x$ and minor axis along $p_y$, the definition of the final momenta $p_{x\mathrm{final}}$ and $p_{y\mathrm{final}}$, and the angular offset $\theta$ are drawn in white. (d),(e) Momentum distributions calculated under the same conditions as (b) and (c), respectively.

Figure 2

Initial and final momentum of photoelectrons along the $y$ axis according to different theories. For the definition of the momenta refer to Eq. (2). The final momentum $p_{y\mathrm{final}}$ (green dashed line) is the same in the nonadiabatic theories developed by Mur et al. [12], Goreslavski et al. [19], and Barth et al. [14]. Identical momentum offset $p_{y\mathrm{initial}}$ at the tunnel exit by Mur and Goreslavski (green solid line) and the momentum offset by Barth et al. before the tunnel barrier (red solid line).

Figure 3

Mapping of final momentum along the $y$ axis, $p_{y\mathrm{final}}$, as a function of intensity. Single trajectory calculations (ST, dashed lines) and CTMC simulations (solid lines) are shown both in the case of zero initial momentum offset (blue) and with positive offset (green). Note the increased momentum, due to the offset, and the reduction in the CTMC calculations due to an out-of-phase ionization.

Figure 4

(a) The analytical formula Eq. (2) with (dashed green line) and without (dashed blue line) the nonadiabatic contribution ($p_{y\mathrm{initial}}$ larger or equal to zero, respectively) is used to fit the ellipticity dependent data (red circles). (b) Final angle $\theta$ obtained from electron momentum distributions shown as a function of intensity together with the curves predicted by the TIPIS model with (green) and without initial offset (blue) for single trajectory calculations (ST, dashed lines) and CTMC calculations (solid lines). The intensities of the experimental data have been scaled according to the selected theory, following the mapping shown in Fig. 3.