Ultrafast optical spectroscopy of superconducting materials

The microscopic degrees of freedom of electron, lattice, spin and orbit play a vital role in the macroscopic properties of superconducting materials. In superconducting systems, especially unconventional superconducting materials, these degrees of freedom lead to enormous collective excitations and ordered states with different energy scales. Examples for the collective excitations are phonons, magnons, charge density waves, spin density waves, spin fluctuations, nematic fluctuations, and so on; ordered states are superconducting state, pseudogap state, nematic phase, antiferromagnetic/ferromagnetic order, and so on. The collective exciations can make vital contribution to the formation of the ordered states. In particular, different types of collective excitations are entangled in the frequency domain and interact with each other, and at the same time are coupled with electrons (or quasiparticles), resulting in the complex and rich physics in the equilibrium and non-equilibrium states. The uniqueness of ultrafast optical spectroscopy is that it covers both a wide energy range and high time resolution. Using the linear and nonlinear optical responses during the interaction between light (electromagnetic waves) and superconducting materials, the quasi-equilibrium or non-equilibrium dynamical properties can be detected and controlled at the resonant or non-resonant conditions. Because of the flexibility of the table-top optical systems, it is not only used in superconducting materials, but also widely employed in various other inorganic and organic material systems. Because the non-equilibrium theory, especially the theoretical research on correlated electronic materials, is still in the stage of rapid development, this review mainly introduces the commonly used table-top ultrafast optical spectroscopy and the related analytical theories that are currently widely used, focusing on discussion of the universal trends and developments emerging from experimental data of the ultrafast optical spectroscopy on superconducting materials, which include the conventional superconductors, cuprate superconductors, iron-based superconductors, and heavy fermion superconductors.