Multidimensional High Harmonic Spectroscopy

We will discuss a novel method for monitoring electronic coherences using ultrafast spectroscopy. This method is 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 using a three-step mechanism. The coherent dynamics can then be probed by the higher order harmonics generated by the delayed probe pulse. A a semi-perturbative 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 the first and the second order responses and investigate nonadiabatic dynamics of conical intersections and avoided crossings. High harmonic echo allows to detect both the population transfer and coherent dephasing dynamics in multidimensional spectra. We are able to selectively produce a delayed harmonic echo originated from partial rephasing of a given pair of bound states which is not possible in traditional echo experiments that rely exclusively on full rephasing of electronic coherence. Furthermore, the nature of the multi-wave mixing in high harmonic regime allow to modify the statistics of light and give rise of quantum squeezing between higher harmonics suitable for higher signal-to-noise ratio measurements of electronic properties in multi-eV range.