Two-Source Double-Slit Interference in Angle-Resolved High-Energy Above-Threshold Ionization Spectra of Diatoms

When an electron from a diatomic molecule undergoes tunneling-rescattering ionization, a novel form of destructive interference can be realized that involves all four geometric orbits that are available to the electron when it is freed, because both ionization and rescattering may take place at the same or at different centers. We find experimentally and confirm theoretically that in orientation-averaged angle-resolved high-order above-threshold ionization spectra the corresponding destructive interference is visible for ${\mathrm{O}}_2$ but not for ${\mathrm{N}}_2$. This effect is different from the suppression of ionization that is well known to occur for ${\mathrm{O}}_2$.

Figure 1

False-color angle-resolved electron energy spectra for ionization of ${\mathrm{N}}_2$ and ${\mathrm{O}}_2$ by a 100 fs 800 nm laser pulse with an estimated peak intensity $I$. Left (right) panels: Experimental (theoretical) results. Upper panels: ${\mathrm{N}}_2$ at $I=9\times {10}^{13}\mathrm{W}/{\mathrm{cm}}^2$. Lower panels: ${\mathrm{O}}_2$ at $I=7\times {10}^{13}\mathrm{W}/{\mathrm{cm}}^2$. The lower right panel presents the contrast $C=[w({\theta }_e)-w(0)]/[w({\theta }_e)+w(0)]$ of the suppression for ${\mathrm{O}}_2$ as a function of intensity for two different values of ${\theta }_e=20°$ and 30°, evaluated by three-dimensional orientation averaging of Eq. (2) for $\pi$ symmetry at the energy corresponding to the cutoff. This panel shows that we have chosen the optimal intensity ($7\times {10}^{13}\mathrm{W}/{\mathrm{cm}}^2$) for the observation of the destructive two-source double-slit interference. The two panels on the upper right present cuts through the experimental (red curves with error bars) and the theoretical (solid blue curves) at 42 (for ${\mathrm{N}}_2$) and 23.5 eV (for ${\mathrm{O}}_2$). They quantitatively assess the quality of the MSFA and clearly demonstrate the suppression for ${\mathrm{O}}_2$ and its absence for ${\mathrm{N}}_2$.

Figure 2

Schematic diagram of the four rescattering $T$-matrix contributions to strong-field ionization of a diatomic molecule. The intermediate (between ionization and rescattering) electron drift momentum ${\mathbf{k}}_s$ is along the laser polarization axis. The final momentum ${\mathbf{p}}_f$ and the relative nuclear coordinate ${\mathbf{R}}_0$ include the angles ${\theta }_e$ and ${\theta }_L$ with respect to the former. In the upper panels the contributions $T^{++}$ and $T^{--}$ are depicted, where the electron rescatters at the same center at which it was born, and the corresponding electron path-length difference $\Delta =R_0\cos ({\theta }_e-{\theta }_L)$ is indicated. The two lower panels show the contributions of the processes where ionization and rescattering occur at different centers. The path-length difference of these two contributions, before rescattering, is $2{\Delta }_L=2R_0\cos {\theta }_L$.

Figure 3

Calculated angle-resolved ATI spectra for ${\mathrm{N}}_2$ (left) and ${\mathrm{O}}_2$ (right) for fixed orientation of the molecular axis for the intensities of Fig. 1. The orientation is at angles of ${\theta }_L=0°$, 30°, 45°, 60°, and 90° from top to bottom. For ${\mathrm{O}}_2$, we used ${\theta }_L=1°$ and 89° in place of 0° and 90°. For the latter angles, the rescattering plateau is entirely absent.