Driving a topological insulator using a Gaussian pulse

A perfectly periodic time-dependent perturbation, such as radiation, when applied to a system at equilibrium can be understood

using Floquet theory and may result in generating topologically non-trivial phases in a system which was trivial to begin with.

However, in a real experiment that relies on pump-probe techniques to study materials, the external perturbation is never perfectly

periodic and has a pulse shape/envelope function. Using actual time-evolved states, we calculate the optical conductivity in presence

of such a drive and compare it to the response calculated using Floquet theory. The conductivity is found to bear a memory of the initial

equilibrium state. This hold even with a slow turning on of the pump and the measurement taken well after the ramp. The response of

the time-evolved system is interpreted as a result of the population of Floquet bands being determined by their overlap with the initial

equilibrium state. In particular, at band inversion points in the Brillouin zone the population of the Floquet bands is inverted as well.