Above-threshold ionization in a strong dc electric field

High-lying Rydberg states of Xe have been ionized using intense $108\mu \text{m}$ radiation from a free-electron laser. Measured two-dimensional photoelectron images reveal significant above-threshold ionization and contain an indirect contribution resulting from the combined action of the atomic Coulomb field, laser field, and dc electric field of the spectrometer on the electron. The observation of indirect ionization contains information about the electron localization directly after the laser excitation and indicates that the experiments are performed in the multiphoton regime of strong-field ionization. The experiments are compared to and interpreted by means of both classical and quantum-mechanical simulations.

Figure 1

Ionization in the presence of an attractive Coulomb potential and a dc electric field $F_{\text{dc}}$ (solid line). The dc electric field (dashed line) lowers the ionization potential from its field-free value to an energy $E=-2\sqrt{F_{\text{dc}}}$. The figure is drawn for the experimental field strength $F_{\text{dc}}=4.57\times {10}^{-8}\text{a}\text{.u}\text{.}$ For this field strength the location of the saddle point in the $\text{Coulomb}+\text{dc}$ field potential occurs at $R=1\sqrt{F_{\text{dc}}}=4.7\times {10}^3\text{a}\text{.u}\text{.}$ Importantly, this distance is significantly larger than the radius that the electron can reach under the influence of the $108\text{−}\mu \text{m}$ ionizing laser field, ruling out that tunneling and over-the-barrier ionization plays a role in the experiment (see text for details).

Figure 2

Experimental arrangement: The dye laser and the FEL move at right angles with respect to each other and with respect to a ${\text{Xe}}^{\ast }$ beam that moves along the detector axis of a velocity map imaging spectrometer. The polarization of the dye laser, $P_{\text{dye}}$, is perpendicular to the plane of the imaging detector, while the polarization of the free-electron laser, $P_{\text{FEL}}$, is in the plane of the imaging detector. This allows recovery of the 3D velocity distribution of the detected electrons by means of an Abel inversion as long as the electron angular distribution does not depend on the dc electric field (see text for details).

Figure 3

(Color online) Experimental 2D images measured for ionization by the $108\text{−}\mu \text{m}$ FEL of Xe atoms that have first been prepared at a range of initial energies (given with respect to the field-free ionization limit) by tuning the wavelength of a dye laser that excited ${\text{Xe}}^{\ast }\left(6s{\left[3/2\right]}_{J=2}\right)$ atoms produced by electron-impact excitation. The polarization of the FEL is along the vertical axis. The experiment was performed in a dc electric field of 235 V/cm $\left(4.57\times {10}^{-8}\text{a}\text{.u}\text{.}\right)$, leading to a saddle point in the $\text{Coulomb}+\text{dc}$ field potential (see Fig. 1) at an energy of $-0.00042\text{a}\text{.u}\text{.}$

Figure 4

Photoelectron spectra derived from the images shown in Fig. 3, showing a series of contributions corresponding to ATI, as well as indirect ionization (indicated by a star) caused by a post-collision interaction of the electron with the ion. The observation of this peak is taken as evidence that the experiment is performed in the multiphoton regime of strong-field ionization (see text for details).

Figure 5

Electron kinetic energies identified in the 2D photoelectron images, plotted as a function of the initial state energy used in the experiment. Branches corresponding to ATI (solid squares) and indirect ionization (open squares) are observed. The solid and dashed lines correspond to predictions from a classical theory assuming an ionization process originating at the nucleus (model C; see text for details).

Figure 6

(Color online) Momentum maps of the ionized electron wave packet calculated at a delay of 120 ps for ionization of Xe atoms prepared at an initial energy of $-0.00084\text{a}\text{.u}\text{.}$ and ionized with a 2-ps $\omega =6\times {10}^{-4}\text{a}\text{.u}\text{.}$ laser pulse with a peak intensity of (a) $5\times {10}^4\text{W}/{\text{cm}}^2$, (b) $5\times {10}^5\text{W}/{\text{cm}}^2$, and (c) $5\times {10}^6\text{W}/{\text{cm}}^2$. Contributions assigned to direct and indirect one-photon ionization and multiphoton ionization are indicated. In the momentum maps a change in the ratio of the direct-to-indirect ionization [comparing the intensity at $\left(p_x=0.,p_z=-0.19\text{a}\text{.u}\text{.}\right)$ to that at $\left(p_x=0,p_z=-0.10\text{a}\text{.u}\text{.}\right)$] can be readily observed. Note that unlike the experiment, in the calculation both the far-infrared laser pulse and the dc electric field were polarized along the $z$ axis.

Figure 7

Power dependence of the direct and indirect one-photon contributions to the ionization yield (scaled to a common value at low intensity), along with that of two- and three-photon contributions in the momentum maps. Importantly, the indirect one-photon contribution retains a linear power dependence well beyond the intensity $\left(\sim 5\times {10}^5\text{W}/{\text{cm}}^2\right)$ where the direct contributions begins to deviate significantly