THz pump-probe spectroscopy: instantaneous response and coherent oscillations

The latest advances in time-resolved spectroscopic techniques, based on the generation of intense ultra-short light pulses, have paved new intriguing ways for the investigation of collective phenomena in many complex systems. In spite of this huge experimental progress, an exhaustive theoretical framework able to connect the measured quantity to the microscopic properties of the material under study is still lacking. With the aim to fill in part this knowledge gap, we provide a general scheme shedding light on some of the most relevant features observed in the experiments, such as the instantaneous response following the squared pump field in wide band insulators, also referred to as THz Kerr effect, and the appearance of time-resolved oscillations at the typical frequencies of different collective modes. We will show how the first aspect can be related to the off-resonant excitation of the electronic population as well as to absorption effects due to the lattice, while the latter is associated with a Raman-like excitation process, explaining both the generation of coherent optical phonons and electronic collective modes, such as charge, amplitude (Higgs) and phase fluctuations in a superconductor.