Crossover of coherent Rabi oscillations in graphene

We study the phenomenon of crossover of Rabi oscillations in graphene as a function of detuning—the difference between the frequency of the incident wave and interband energy (2vF|k|2vF|k|). It is shown by comparison with an exactly solved model with bands having linear dispersion but lacking pseudospin that this crossover is unique to graphene, attributable to the pseudospin character of the graphene hamiltonian. A group theoretic argument for why this model is solvable is given. We compute the nonlinear current using our formalism, the main prediction being the threshold behavior (with exponent equal to 1/2) of the slowly varying part of the current in frequency domain with threshold frequency being 2ωR2/ω (‘anomalous’ Rabi frequency) where ωRωR is the Rabi frequency for zero detuning. The novelty of our approach is the introduction of an alternative to the rotating wave approximation (RWA) (called asymptotic RWA here) which is argued to be important in demonstrating this crossover. We provide an interpolation method between these two regimes, that shows novel phenomena attributable to harmonic generation. A fully numerical solution to the Bloch equations verifies the analytical results and the various approximation schemes.