Quantum correlation of electron and ion energy in the dissociative strong-field ionization of ${\mathrm{H}}_2$

We report on the strong field ionization of ${\mathrm{H}}_2$ by a corotating two-color laser field. We measure the electron momentum distribution in coincidence with the kinetic energy release (KER) of dissociating hydrogen molecules. In addition to a characteristic half-moon structure, we observe a low-energy structure in the electron momentum distribution at a KER of about 3.5 eV. We speculate that the outgoing electron interacts with the molecular ion, despite the absence of classical recollisions under these conditions. Time-dependent density functional theory simulations support our conclusions.

Figure 1

(a) The Lissajous curve of the laser electric field and the corresponding negative vector potential. The arrows indicate the temporal evolution of the laser electric field. The dots indicate the peak of $|\vec{E}\left(t\right)|$ and the corresponding negative vector potential. (b) Measured electron momentum distribution for the laser field that is shown in (a) with a logarithmic color scale.

Figure 2

(a) Shows the measured kinetic energy release (KER) distribution for the reaction ${\mathrm{H}}_2\to \mathrm{H}+{\mathrm{H}}^{+}+e^{-}$. (b)–(d) show the measured electron momentum distributions which are restricted to the measured KER intervals that are indicated in (a). The three-dimensional (3D) electron momentum distributions are represented using five semitransparent isosurfaces encoding the intensity of the 3D histogram by color. The $p_y{p}_z$ plane is the polarization plane.

Figure 3

Experimental data on the strong field dissociation of ${\mathrm{H}}_2$. (a) shows the energy of the electron as a function of the KER. In (b) each column of the distribution in (a) is normalized to a maximum of one. The horizontal line in (b) guides the eye and the green square highlights the KER region in which there is the low-energy structure. (b) reveals that low-energy electrons ($E_{\mathrm{elec}}<3\mathrm{eV}$) are very pronounced for 3 eV $<$ KER $<$ 6 eV. (c) shows the potential energy of the ground state of ${\mathrm{H}}_2$ and two states of ${\mathrm{H}}_2^{+}$ as a function of the internuclear distance. The purple arrow marks the strong field transition from the ground state to the $1s{\sigma }_g$ state. Two possible transitions from the $1s{\sigma }_g$ to the $2p{\sigma }_u$ curve are marked by a blue and a green arrow, respectively. The KERs that result from these two transitions are marked by colored areas in the KER distribution in (d). (d) shows the same data as Fig. 2.

Figure 4

Theoretical data on the ionization of ${\mathrm{H}}_2$ in a CoRTC field. (a) shows the electron momentum distribution with a logarithmic color scale that is obtained using a time-dependent density functional theory (TDDFT) approach. (b) shows the ionization probability as a function of the final electron energy and the internuclear distance $R$ (upper horizontal axis) of the ${\mathrm{H}}_2$ molecule. ATI peaks were removed by applying a low-pass filter to the electron energy distribution. Each column of the distribution is normalized to a maximum of one. The lower horizontal axis shows the corresponding estimated KER, which is derived from the $2p{\sigma }_u$ curve (see text). The black line indicates the ponderomotive energy $U_p=5.2\mathrm{eV}$. The green square highlights the same KER region as in Fig. 3.