# Theory of coherent oscillations detection in THz pump-probe spectroscopy: from phonons to electronic collective modes

## TL;DR

This paper develops a theoretical framework linking coherent oscillations in THz pump-probe spectroscopy to a convolution of the pump field with a Raman-like kernel, explaining experimental observations across various condensed matter systems.

## Contribution

It introduces a general theoretical scheme for understanding coherent oscillations in THz pump-probe spectroscopy, applicable to phonons and electronic collective modes.

## Key findings

- The scheme accurately explains existing experimental data.
- It applies to phonons, charge, and Higgs modes in different materials.
- Provides insights for designing future experiments.

## Abstract

Time-resolved spectroscopies using intense THz pulses appear as a promising tool to address collective electronic excitations in condensed matter. In particular recent experiments showed the possibility to selectively excite collective modes emerging across a phase transition, as it is the case for superconducting and charge-density-wave (CDW) systems. One possible signature of these excitations is the emergence of coherent oscillations of the differential probe field in pump-probe protocols. While the analogy with the case of phonon modes suggests that the basic underlying mechanism should be a sum-frequency stimulated Raman process, a general theoretical scheme able to describe the experiments and to define the relevant optical quantity is still lacking. Here we provide this scheme by showing that coherent oscillations as a function of the pump-probe time delay can be linked to the convolution in the frequency domain between the squared pump field and a Raman-like non-linear optical kernel. This approach is applied and discussed in few paradigmatic examples: ordinary phonons in an insulator, and collective charge and Higgs fluctuations across a superconducting and a CDW transition. Our results not only account very well for the existing experimental data in a wide variety of systems, but they also offer an useful perspective to design future experiments in emerging materials.