Detecting electronic coherences by time-domain high-harmonic spectroscopy

Ultrafast spectroscopy is capable of monitoring electronic and vibrational states. For electronic states a few eV apart, an X-ray laser source is required. We propose an alternative method based on the time-domain high-order harmonic spectroscopy where a coherent superposition of the electronic states is first prepared by the strong optical laser pulse. The coherent dynamics can then be probed by the higher-order harmonics generated by the delayed probe pulse. The high nonlinearity typically modeled by the three-step mechanism introduced by Lewenstein and Corkum can serve as a recipe for generation of the coherent excitation with broad bandwidth. The main advantage of the method is that only optical (non–X-ray) lasers are needed. A semiperturbative model based on the Liouville space superoperator approach is developed for the bookkeeping of the different orders of the nonlinear response for the high-order harmonic generation using multiple pulses. Coherence between bound electronic states is monitored in the harmonic spectra from both first- and second-order responses.