Real-time photoinduced quasi-particle relaxation of superconductors

Ultrafast optical phenomena are of fundamental importance in the investigation of electronic dynamics of metals and superconductors [1]. By considering a model Hamiltonian with electron-boson coupling of a superconductor exposed to a time-dependent laser field, we calculate the current density, which can be expressed in terms of the quasi-particle density matrices. The time evolution of these density matrices is derived within a mean-field approximation using the equation-of-motion approach and is numerically investigated with Runge-Kutta method. we discuss the consequence of the $d$-wave pairing symmetry in the quasi-particle relaxation process. \\[3pt] [1] R. D. Averitt and A. J. Taylor, J. Phys: Condensed Matter 14, R1357 (2002).