Transient Impulsive Electronic Raman Redistribution

Resonant Raman excitation by ultrafast vacuum ultraviolet laser pulses is a powerful means to study electron dynamics in molecules, but experiments must contend with linear background ionization: frequencies high enough to reach resonant core-valence transitions will usually ionize all occupied orbitals as well, and the ionization cross sections are usually dominant. Here we show that attosecond pulses can induce a process, transient impulsive stimulated Raman scattering, which can overwhelm valence ionization. Calculations are performed for atomic sodium, but the principal is valid for many molecular systems. This approach opens the path for high-fidelity multidimensional spectroscopy with attosecond pulses.

Figure 1

One-photon single ionization cross section of ground state Na in the resonance region. The black line shows the series of resonance due to $({}^{1}P)ns$ or $nd$ states imbedded in the continuum, and the red line is the resonances due to $({}^{3}P)ns$ or $nd$ states.

Figure 2

The electronic Raman transition probability for Na atom as a function of maximum laser intensity ($I_0$). The final state population from a model time-dependent calculation is also shown. The pulse duration (FWHM) is 1 fs and the central frequency is 35.0 eV.

Figure 3

Raman transition probability (black line) and one-photon single ionization probability (red line) in Na atom as a function of maximum laser intensity. The result obtained using perturbation theory is shown. Pulse parameters are equal to Fig. 2.

Figure 4

Raman transition probability and single ionization probability as a function of the central frequency of the pulse for different pulse durations. $I_0=5\times 10^{15}\mathrm{W}/{\mathrm{cm}}^2$ for the 1 fs pulse, and the total pulse energy is kept constant for each pulse (see text).

Figure 5

The electronic Raman resonances for Na atom is plotted as a function of both incident (black lines) and emitted (red lines) photon energies. We also plot the energy bandwidth of the Gaussian shaped pulse envelope for 1, 3, and 5 fs pulses.