A theoretical study of pump–probe experiment in single-layer, bilayer and multilayer graphene

The pump–probe experiment is typically used to study relaxation phenomena in nonlinear optical systems. Here we use it as a tool to study the phenomenon of anomalous Rabi oscillations in graphene that was predicted recently in single-layer graphene. Unlike conventional Rabi oscillations, anomalous Rabi oscillations are unique to graphene (and possibly to surface states of topological insulators (TIs)), attributable to the pseudospin (conventional spin for TI) degree of freedom and Dirac-fermion character of the graphene system. A pump pulse of a finite duration long enough to contain a large number of cycles induces a current density that oscillates with the frequency of the pump pulse. The amplitude associated with these fast oscillations is seen to exhibit much slower oscillations with a frequency given by 2ωR2/ω\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}${ 2 \omega ^2_{\mathrm {R}} }/{ \omega } $\end{document} – the anomalous Rabi frequency, where ωR is the conventional Rabi frequency and ω is the frequency of the external pump field. This effect is easily probed by a probe pulse subsequent to the pump, where it manifests itself as periodic oscillations of the probe susceptibility as a function of pump duration at each probe frequency. Alternatively, it is also seen as an oscillatory function of the pump–probe delay with other variables remaining fixed. This period corresponds to the anomalous Rabi frequency. An analysis of the previously reported experimental data confirms the presence of anomalous Rabi oscillations in graphene.