Ellipticity-dependent sequential over-barrier ionization of cold rubidium

We perform high-resolution measurements of momentum distribution on ${\mathrm{Rb}}^{n+}$ recoil ions up to charge state $n=4$, where laser-cooled rubidium atoms are ionized by femtosecond elliptically polarized lasers with the pulse duration of 35 fs and the intensity of $3.3\times {10}^{15}\mathrm{W}/\mathrm{c}{\mathrm{m}}^2$ in the over-barrier ionization (OBI) regime. The momentum distributions of the recoil ions are found to exhibit multiband structures as the ellipticity varies from the linear to circular polarizations. The origin of these band structures can be explained quantitatively by the simple man model based on the OBI mechanism and dedicated classical trajectory Monte Carlo simulations with Heisenberg potential. Specifically, with back analysis of the classical trajectories, we reveal the ionization time and the OBI geometry of the sequentially released electrons, disentangling the mechanisms behind the tilted angle of the band structures. These results indicate that the classical treatment can describe the strong-field multiple ionization processes of alkali atoms.

Figure 1

Simplified schematic view of the MOTRIMS experimental setup. Rubidium atoms are precooled within a typical 2D MOT configuration and pushed by the pushing laser into the reaction region, where the atoms are further cooled and trapped in a standard 3D MOT and subsequently ionized by back-reflected femtosecond-laser pulses. The polarization and the propagation directions of the laser are defined as in the $y$ and $z$ directions, respectively. Electric fields (∼1 V/cm) guide the recoil ions to time- and position-sensitive detectors.

Figure 2

Measured RIMDs in the polarization plane for different ellipticities ε (columns) from linearly polarized to almost circularly polarized fields for double, triple, and quadruple ionizations (rows) of neutral Rb atoms. The major/minor polarization direction is along the $y$/$x$ axis. Presented RIMDs are sliced in the propagation direction of the laser. The arrows indicate the tilted angles and dashed circles represent predicted momenta based on the SM-OBI calculations.

Figure 3

One-dimensional momentum spectra of ${\mathrm{Rb}}^{2+}$ [panel (a)], ${\mathrm{Rb}}^{3+}$ [panel (b)] and ${\mathrm{Rb}}^{4+}$ [panel (c)] ions, sliced in the $y$ direction and projected onto the $x$ axis (along the minor axis) at ellipticity $\varepsilon =0.7$ in Fig. 2. The vertical arrows indicate the peak locations expected for the classical calculations, as discussed in the text. The four peaks in panel (c), from left to right, correspond to $p_{\mathrm{i}}^{4+}\left(1\right)=\left(-p_{\mathrm{e}}^2-p_{\mathrm{e}}^3+p_{\mathrm{e}}^4\right)$ (peak I), $p_{\mathrm{i}}^{4+}\left(2\right)=\left(p_{\mathrm{e}}^2-p_{\mathrm{e}}^3+p_{\mathrm{e}}^4\right)$ (peak II), $p_{\mathrm{i}}^{4+}\left(3\right)=\left(-p_{\mathrm{e}}^2+p_{\mathrm{e}}^3+p_{\mathrm{e}}^4\right)$ (peak III), and $p_{\mathrm{i}}^{4+}\left(4\right)=\left(p_{\mathrm{e}}^2+p_{\mathrm{e}}^3+p_{\mathrm{e}}^4\right)$ (peak IV), respectively. $p_{\mathrm{i}}^{n+}$ and $p_{\mathrm{e}}^m$ are defined as the momenta of recoil ion in charge state $n+$ and the $m\mathrm{th}$ ionizing electron, respectively.

Figure 4

The simulated ellipticity-dependent RIMDs of Rb for double, triple, and quadruple ionizations at the intensity of $3.3\times {10}^{15}\mathrm{W}/\mathrm{c}{\mathrm{m}}^2$.

Figure 5

The same as Fig. 4 but at $5.0\times {10}^{14}\mathrm{W}/\mathrm{c}{\mathrm{m}}^2$. The quadruple ionization events are rare at this intensity and thus are not shown.

Figure 6

Typical trajectory of a sequential ionization by an elliptically polarized strong laser field at $5.0\times {10}^{14}\mathrm{W}/\mathrm{c}{\mathrm{m}}^2$ and $\varepsilon =0.7$. The ionization time, defined as the instant when the energy of the electron becomes positive, is marked by the solid circles in (a) and the corresponding ionization geometries are shown in (b). Note, $e_2$ and $e_3$ are defined as the second and the third ionized electrons.

Figure 7

The joint distributions of the ionization time and the electron distance to the nucleus (upper row). The white curves illustrate the waveform of the electric field $\left|E\left(t\right)\right|$, which explains the subcycle stripe structures at lower ellipticities. In panel (f), the sequential ionization time distributions of the second and third ionized electrons are shown and the most probable OBI points are marked with red crosses. It can be seen that the depletion and saturation effects are naturally included in our CTMC-H simulations. The exit geometries in the polarization plane are shown in the middle (second ionization) and the lower (third ionization) rows, respectively. The laser parameters are the same as that in Fig. 6.