Attosecond streaking of Cohen-Fano interferences in the photoionization of ${\mathrm{H}}_2^{+}$

We present a numerical ab-initio simulation of the time delay in the photoionization of the simplest diatomic molecule ${\mathrm{H}}_2^{+}$ as observed by attosecond streaking. We show that the strong variation of the Eisenbud-Wigner-Smith time delay $t_{\mathrm{EWS}}$ as a function of energy and emission angle becomes observable in the streaking time shift $t_{\mathrm{S}}$ provided laser field induced components are accounted for. The strongly enhanced photoemission time shifts are traced to destructive Cohen-Fano (or two-center) interferences. Signatures of these interferences in the streaking trace are shown to be enhanced when the ionic fragments are detected in coincidence.

Figure 1

(a) Typical streaking spectrogram for ionization of ${\mathrm{H}}_2^{+}$ by a 130-eV XUV pulse [${\theta }_x=0^{\circ }$, ${\tau }_{\mathrm{XUV}}=400$ as (FWHM)] probed by a 800-nm two-cycle streaking field with intensity $I_{\mathrm{IR}}={10}^{11}W/{\mathrm{cm}}^2$ for electron emission along the polarization axis of the streaking field $\left({\theta }_e=0^{\circ }\right)$ and fixed internuclear distance $R=3$a.u. (b) Extracted streaking delays $t_{\mathrm{S}}$ for ${\mathrm{He}}^{+}$ (red circles), ${\mathrm{H}}_2^{+}$ at $R=0.1$a.u. (blue diamonds), and ${\mathrm{H}}_2^{+}$ at $R=3.0$a.u. (black squares) for pulse parameters ${\tau }_{\mathrm{XUV}}=600$ as (FWHM) and $I_{\mathrm{IR}}={10}^{8}W/{\mathrm{cm}}^2$.

Figure 2

EWS delay $t_{\mathrm{EWS}}$ in the $(E,R)$ plane for emission along the internuclear axis ${\theta }_e=0^{\circ }$ and the XUV pulse polarized parallel to the internuclear axis, ${\theta }_x=0^{\circ }$. The EWS delays that are contained in the streaking results of Fig. 1 [Eq. (1)] correspond to cuts for constant $R$ (dashed line for $R=3)$.

Figure 3

EWS time delays of ${\mathrm{H}}_2^{+}$ at the equilibrium distance $R$ = 2 a.u., plotted as a function of electron energy $E$ and ejection angle ${\theta }_e$ [$t_{\mathrm{EWS}}\left(E,{\theta }_e\right)$] for the XUV pulse polarized (a) parallel $({\theta }_x$ = $0{}^{\circ })$ or (c) perpendicular $({\theta }_x$ = $90{}^{\circ })$ with respect to the molecular axis. The corresponding single-photon differential ionization cross sections (DCS) in (b) and (d) are plotted on a logarithmic scale. A cut of the DCS at ${\theta }_e=0$ for the case ${\theta }_x=0$ is plotted along with the phase of the transition matrix element in (e) and along with the EWS delay $t_{\mathrm{EWS}}$ in (f).

Figure 4

Comparison between the location of the minima in the differential photoionization cross section (DCS) in the $(E,cos{\theta }_e)$ plane with the prediction of the two-center interference model according to $\sqrt{2E}R\cos {\theta }_e=(2n+1)\pi$ [see inset in (a)] for different $n$. The DCS is given for a Franck-Condon transition at (a) $R=2$ and (b) $R=5$. Note that the extraction of well-defined minima from the very small DCS is not always possible, giving rise to the discontinuities.

Figure 5

(a) Comparison between the differential cross section (DCS) at fixed internuclear equilibrium distance $R=2$ and averaged over the vibrational ground-state distribution $W_0$. (b) Expectation values ${\langle t_{\mathrm{EWS}}\rangle }_R$ and ${\langle t_{\mathrm{S}}\rangle }_R$ after averaging over the vibrational ground-state distribution $W_0$ (squares) and the distribution $W_{\Delta }$ (triangles) postselected from the Coulomb explosion of the molecular fragments. The XUV pulse duration in the streaking simulations is ${\tau }_{\mathrm{XUV}}=600$ as (FWHM) and the intensity of the probing 800-nm field is $I_{\mathrm{IR}}={10}^{8}W/{\mathrm{cm}}^2$.