Unexpectedly broad photoelectron spectrum as a signature of ultrafast electronic relaxation of Rydberg states of carbon dioxide

The dynamics of ${\mathrm{CO}}_2$ excited into Rydberg states lying 0.2 eV below the ionization threshold is studied by means of time resolved photoelectron imaging. Over 3 eV broad photoelectron spectra are measured for all pump-probe delay times. Quantum mechanical calculations demonstrate that the spectral broadening is due to ultrafast electronic relaxation of Rydberg states and identify the likely relaxation pathways. Experiment and theory bracket the relaxation time between 15 and 65 fs. A weak time independent ionization signal is attributed to ${\mathrm{CO}}_2$ trapped in near-threshold triplet states.

Figure 1

(a) The experimental absorption spectrum of ${\mathrm{CO}}_2$. The horizontal axis shows the cross sections on a logarithmic scale (powers of ten are indicated). Two combs indicate experimentally assigned [19] dipole allowed states ${}^1\mathrm{\Sigma }_u^{+}$ and ${}^1\mathrm{\Pi }_u$. Black sticks are the zero-point energy corrected ab initio vertical excitation energies. Stick heights are proportional to the transition dipole moment. Gray strip indicates the spectral width of the pump laser. Schematics in the top illustrates the kinetic model of Eq. (4); “S” and “T” stand for singlet and triplet electronic manifolds. (b) Energies of calculated singlet electronic states as functions of one bond length $R_{\mathrm{CO}}$. The second bond is fixed at 2.2 bohr, and the valence angle is ${179}^{\circ }$. The ground state of ${\mathrm{CO}}_2{}^{+}$ is shown with a thick black line. Vertical red arrows show the pump and the probe pulses.

Figure 2

(a) Pump-probe photoelectron spectra for the delay from $-200$–2500 fs on the binding and kinetic energy scales. (b) Photoelectron spectra at 190 fs, 700 fs, and 1300 fs (solid lines); the expected spectrum at 0 fs (dotted line) centered at $e\mathrm{BE}$ = 13.8 eV with a FWHM of 0.44 eV. Horizontal arrows represent the $e\mathrm{BE}$-dependent experimental resolution. (c) Theoretical photoelectron spectrum for the delay time of 50 fs (black); red dotted line is the spectrum of the initial excitation. (d) Time profile of the photoelectron intensity at $e\mathrm{BE}$ = 14.4 eV. Red and blue dotted lines are the components $i=1$ and 2 in Eq. (4); black solid line is their sum. (e) Anisotropy parameter ${\beta }_2$ as a function of $\tau$ for $e\mathrm{BE}$ = 14.2 eV. Dashed line is a single exponential fit with the time constant of 200 fs.

Figure 3

(a) Energies of diabatic electronic states ${}^1{A}^{\prime \prime }$ of ${\mathrm{CO}}_2$ shown along one bond length $R_{\mathrm{CO}}$. The second bond is fixed at 2.2 bohr, and the valence angle is ${179}^{\circ }$. States which belong to series not converging to ${\mathrm{CO}}_2{}^{+}\left(X{}^2{\mathrm{\Pi }}_g\right)$ are shown with red. Gray dots are ab initio energies. (b) The calculated time dependent population of the initially excited bright electronic states of ${\mathrm{CO}}_2$. The results for two diabatic coupling strengths, $\lambda =0.01$ eV (blue) and 0.02 eV (brown), are shown. (c) The spectral width of the quantum mechanical photoelectron spectra versus the delay time. Dashed line is a fit to an exponential function $1.08-exp(-t/{\tau }_e)$ with ${\tau }_e=65.0$ fs.

Figure 4

Decay associated spectra $D_1$ (black; right intensity axis) and $D_2$ (red; left intensity axis) as functions of the binding energy. Shaded areas indicate fitting errors.

Figure 5

(a) The photoelectron spectra plotted using the components $D_1$ and $D_2$. (b)–(d) Simulated spectra obtained by adding a component $D_0$ representing the initially excited Rydberg states. (e) The experimental spectrum.

Figure 6

Two-dimensional maps of the anisotropy parameters ${\beta }_2$ (a) and ${\beta }_4$ (b) as functions of the time delay and the binding energy.