Probing calculated ${\text{O}}_2{}^{+}$ potential-energy curves with an XUV-IR pump-probe experiment

We study dissociative photoionization of molecular oxygen in a kinematically complete XUV-IR pump-probe experiment. Detecting charged fragments and photoelectrons in coincidence using a reaction microscope, we observe a pump-probe delay-dependent yield of very low energetic ${\mathrm{O}}^{+}$ ions which oscillates with a period of $40\mathrm{fs}$. This feature is caused by a time-dependent vibrational wave packet in the potential of the binding ${\mathrm{O}}_2{}^{+}\left(a{}^4\Pi _u\right)$ state, which is probed by resonant absorption of a single infrared photon to the weakly repulsive ${\mathrm{O}}_2{}^{+}\left(f{}^4\Pi _g\right)$ state. By quantitative comparison of the experimental kinetic-energy-release (KER) and quantum-beat (QB) spectra with the results of a coupled-channel simulation, we are able to discriminate between the calculated adiabatic ${\mathrm{O}}_2^{+}$ potential-energy curves (PECs) of Marian et al. [Marian, Marian, Peyerimhoff, Hess, Buenker, and Seger, Mol. Phys. 46, 779 (1982)] and Magrakvelidze et al. [Magrakvelidze, Aikens, and Thumm, Phys. Rev. A 86, 023402 (2012)]. In general, we find a good agreement between experimental and simulated KER and QB spectra. However, we could not reproduce all features of the experimental data with these PECs. In contrast, adjusting a Morse potential to the experimental data, most features of the experimental spectra are well reproduced by our simulation. By comparing this Morse potential to theoretically predicted PECs, we demonstrate the sensitivity of our experimental method to small changes in the shape of the binding potential.

Figure 1

Selection of ${\mathrm{O}}_2{}^{+}$ PECs from Ref. [10]. We consider (i) a vibrational wave packet that oscillates within the ${\mathrm{O}}_2{}^{+}\left(a{}^4\Pi _u\right)$ potential (bold green solid curve) and is probed to the ${\mathrm{O}}_2{}^{+}\left(f{}^4\Pi _g\right)$ PEC (bold green dashed curve) and (ii) predissociation out of the ${\mathrm{O}}_2{}^{+}\left(B{}^2\Sigma _g^{-}\right)$ state (bold red dash-dotted curve).

Figure 2

Relevant ${\mathrm{O}}_2{}^{+}$ PECs. The neutral ${\mathrm{O}}_2$ ground-state potential (black curve) is taken from Ref. [14]. A Morse potential (blue dash-dotted curve) has been adjusted to our experimentally observed quantum-beat frequency and revival time. Relevant vibrational states within this potential are plotted as red horizontal lines. The potentials of the binding $a{}^4\Pi _u$ state are taken from Refs. [8] (red [dark gray] curve) and [10] (green [light gray] curve). Absorption of a single IR photon transfers population to the repulsive ${\mathrm{O}}_2{}^{+}\left(f{}^4\Pi _g\right)$ state taken from Refs. [8] (red [dark gray] curve) and [10] (green [light gray] curve). The dashed green curve is the latter curve shifted by 0.08 a.u. towards larger internuclear distances.

Figure 3

Schematic of the reaction microscope and the interferometer for the generation of mutually delayed XUV pump and IR probe pulses, including a microchannel-plate detector (MCP), an aluminum filter (Al filter), and a high-harmonic-generation target (HHG target). The parallel homogeneous electric and magnetic fields within the spectrometer are represented by the white arrow.

Figure 4

(a) Number of detected ${\mathrm{O}}^{+}$ fragments as a function of pump-probe delay and $E_{\text{KER}}$. (b) Projection of events within the black box in panel (a) onto the time-delay axis. For positive delays, the XUV pulse precedes the IR pulse.

Figure 5

(a) QB spectrum of the data shown in Fig. 4. The distinct lines in the QB energy result from the oscillatory behavior of the ${\mathrm{O}}^{+}$ yield as a function of the time delay. (b) Amplitude of the Fourier transform of the delay-dependent yield of low energetic ${\mathrm{O}}^{+}$ ions as a function of $cos\left(\theta \right)$. The angle $\theta$ designates the orientation of the molecular axis relative to the identical linear polarization directions of the XUV and IR pulses.

Figure 6

Simulated yield of ${\mathrm{O}}^{+}$ fragments as a function of pump-probe delay obtained with a coupled-channel simulation involving different sets of PECs. (a) Yield as a function of pump-probe delay and $E_{\text{KER}}$ using the binding ${\mathrm{O}}_2{}^{+}\left(a{}^4\Pi _u\right)$ potential from Ref. [8] (red [dark gray] curve in Fig. 2) and the repulsive ${\mathrm{O}}_2{}^{+}\left(f{}^4\Pi _g\right)$ PEC adapted from Ref. [10] (green [light gray] dashed curve in Fig. 2). (b) Projection of the lower $E_{\text{KER}}$ band in panel (a) onto the time-delay axis. (c) Same as panel (b) but for the binding $a{}^4\Pi _u$ and the repulsive $f{}^4\Pi _g$ PECs from Ref. [10] (green [light gray] solid curves in Fig. 2). (d) Same as (b) but using a Morse potential (blue dash-dotted curve curve in Fig. 2) and the repulsive $f{}^4\Pi _g$ PEC adapted from Ref. [10] (green [light gray] dashed curve in Fig. 2).

Figure 7

QB spectra of the simulated ${\mathrm{O}}^{+}$ yield as a function of $E_{\text{KER}}$. (a) Obtained by using the binding ${\mathrm{O}}_2{}^{+}\left(a{}^4\Pi _u\right)$ potential from Ref. [8] (red [dark gray] curve in Fig. 2) and the repulsive ${\mathrm{O}}_2{}^{+}\left(f{}^4\Pi _g\right)$ PEC adapted from Ref. [10] (green [light gray] dashed curve in Fig. 2). (b) Obtained by using the binding $a{}^4\Pi _u$ and the repulsive $f{}^4\Pi _g$ PECs from Ref. [10] (green [light gray] solid curves in Fig. 2). (c) Obtained by using a Morse potential (blue dash-dotted curve curve in Fig. 2) and the repulsive $f{}^4\Pi _g$ PEC adapted from Ref. [10] (green [light gray] dashed curve in Fig. 2).

Figure 8

(a) QB spectrum of photoelectrons measured in coincidence with low energetic ${\mathrm{O}}^{+}$. Plotted is the Fourier amplitude as a function of the QB energy and the photoelectron kinetic energy $E_e$. (b) Red bold curve: Projection of the QB signal at $E_{\mathrm{QB}}\approx 0.1$ eV shown in panel (a) onto the $E_e$ axis. Blue bold dashed curve: Projection of the dc component at $E_{\mathrm{QB}}<0.005$ eV onto the $E_e$ axis. For better comparison the curves in panel (b) are smoothed and normalized. In addition schematic envelopes of the spectra are shown (thin red solid curve and blue dashed curve).