Numerical method to compute optical conductivity based on pump-probe simulations

A numerical method to calculate optical conductivity based on a pump-probe setup is presented. Its validity and limits are tested and demonstrated via the concrete numerical simulations on the half-filled one-dimensional extended Hubbard model both in equilibrium and out of equilibrium. By employing either a step- or a Gaussian-like probing vector potential, it is found that in nonequilibrium, the method in the narrow-probe-pulse limit can be identified with variant types of linear response theory, which, in equilibrium, produce identical results. The observation reveals the underlying probe-pulse dependence of the optical conductivity calculations in nonequilibrium, which may have its applications in the theoretical analysis of ultrafast spectroscopy measurements.