Off-resonance-enhanced polarization control in two-color atomic ionization

We investigate a polarization control scheme in two-color two-photon atomic ionization. Experiments employing free-electron laser or high-order harmonic generation sources have shown light polarization dependencies in above threshold ionization of atoms assisted with an IR field. These were mostly performed at relatively high photoelectron energies where the soft-photon approximation remains valid. We use here a perturbation theory approach to show the larger degree of control that can be attained when the short wavelength photon energy is below the ionization threshold. This largely unexplored energy region offers unique possibilities to achieve polarization control of the reaction.

Figure 1

Left panel: Schematic representation of the two-color two-photon absorption process in helium. Upon absorption of the EUV photon, a bound electron is promoted to a continuum (intermediate) state. The further absorption of a photon from the IR source leaves the photoelectron in its final state, with energy $E_f$ (path A). Additionally, as the EUV and IR sources overlap in time, the time-reversed reaction, accounting for the dressing of the initial state by the IR field (path B), must be taken into account. Right panel: Relative sideband intensity modulation as a function of the relative polarization angle $\mathrm{\Theta }$ between the fields. The full red dots correspond to previous experimental results [9] (with error bars) and the black full line corresponds to second-order perturbation theory results (see main text).

Figure 2

(a), (b) Intensity modulation ($\mathrm{\Delta }$) as a function of the photoelectron energy. Green full line corresponds to the hydrogenlike perturbation theory model explained in the main text, therefore assuming infinitely long pulses ($T\to \infty$). Red filled symbols (squares, triangles, and circles) correspond to experimental data of previous studies shown in the legend. Blue filled squares are the theoretical results extracted for helium from the data presented in Ref. [13]. Orange (lower) shadow region in panels (a) and (b) corresponds to the situation where $S_2>S_0$. Violet upper shadow region corresponds to $S_0>S_2$, with $S_0$ and $S_2$ being the modulus squared value of the radial matrix elements (RME) associated to emission of an electron in the $s$ and $d$ partial wave, respectively. Vertical dashed thin lines in (a) and (c) indicate the position of the minima for each partial wave. Open circles in panel (a) indicate the energy position of the excited states for the H atom ($n=4,n=5,$ etc.). (c), (d) Modulus squared of the radial partial wave amplitudes as a function of the photoelectron energy. The inset in panel (d) show the energetics in H and He atom. The energy differences between the excited states, as we can see, are very close in energy.

Figure 3

Absolute value of (radial) transition matrix elements corresponding to individual intermediate bound states, and continuum states for a hydrogenlike atom. For clarity purposes, we indicate positive values by thin lines and plus symbols. Negative values are indicated by the dashed lines of the same color. The vertical dashed lines indicate position of the resulting minima shown in Fig. 2.

Figure 4

Intensity modulation $\mathrm{\Delta }$ as a function of the photoelectron energy, for different pulse durations of both the EUV and the IR dressing fields. Symbols with error bars correspond to the experimental data from [21].