Optical conductivity and charge fluctuation spectroscopy in the time domain

Using ultrashort laser pulses it is possible to study the dynamics of many-body systems in the time domain. The response functions are often two-particle correlation functions, including optical or terahertz transmission spectroscopy (current) and charge fluctuation spectroscopy momentum resolved EELS (charge). We have studied two-particle response functions using functional derivatives within a non-equilibrium Keldysh Green’s function method. This has several advantages over common approaches, most notably the natural inclusion of vertex corrections. We present the equilibrium and non-equilibrium response of a few model systems including electrons interacting with each other and with a bath of phonons, and discuss the implications for experiments.