Role of nuclear-electronic coupling in attosecond photoionization of ${\mathrm{H}}_2$

The separation of electronic and nuclear dynamics due to differing timescales is a useful concept for understanding ground-state molecular systems. However, coupling between these degrees of freedom is critical to understanding the evolution of most excited-state systems. We measure two-photon ionization delays of ${\mathrm{H}}_2$ and compare to calculations of the same measurement in a frozen-nuclei approximation. We find discrepancies between the vibrationally resolved measurement and bond-length-dependent theory, suggesting that nuclear motion affects ${\mathrm{H}}_2$ photoionization on attosecond timescales. We ascribe our observation to nuclear-electronic channel coupling between continuum vibrational states. Our results demonstrate that nuclear-electronic coupling cannot be neglected in the sudden ionization of molecules containing light atoms.

Figure 1

Schematic for photoionization by a train of attosecond XUV pulses (APT) in the presence of a weak IR field, resulting in our ${\mathrm{H}}_2$ RABBITT measurement. The APT consists of harmonics up to 30 eV (purple), which drives photoionization in ${\mathrm{H}}_2$ molecules for frequencies above the ionization threshold (i.e., harmonics 11–19). The emitted photoelectrons interact with the weak IR field to produce sideband features, illustrated graphically in the inset. The far right-hand side of the inset shows the measured photoelectron spectrum for the combined XUV/IR field with no retardation voltage on the electron spectrometer (see text).

Figure 2

Two-color photoelectron spectrogram of ${\mathrm{H}}_2$. The bottom panel shows the photoionization spectrum of ${\mathrm{H}}_2$ as a function of XUV/IR time delay, displayed as a percent difference from the time-averaged photoelectron spectrum. The pump/probe oscillations are visible on the time delay axis and vibrational state peaks are visible in the energy axis. A combination of $\omega$ and $2\omega$ oscillations is visible; the $2\omega$ oscillations are isolated by Fourier analysis and used for RABBITT analysis (see Supplemental Material [33]). The amplitudes in the top panel demonstrate our vibrational resolution in each sideband. The black dotted curves (left axis) show the normalized, delay-averaged XUV/IR spectrum and the blue curves (right axis) show the Fourier amplitude of the $2\omega$ oscillations. Each sideband was measured as separate data sets, each with different electron retardation voltages, to optimize spectral resolution (labeled on plot).

Figure 3

Two-photon ionization delays for ${\mathrm{H}}_2$. The measured two-photon ionization delay is extracted from Fig. 2 (black circles). This is compared to fixed-nuclei TDSE simulation for three different nuclear separations $R=1.4,1.45,1.5$ a.u. (red triangle, red asterisk, and red square, respectively). Each $R$ simulation is connected by interpolation (red, dashed line). The top panels show a closer view of the bottom panel for each sideband of the RABBITT measurement.