Properties of collective Rabi oscillations with two Rydberg atoms

Motivated by experimental advances [e.g. A. Ga{\"e}tan {\it et.al.} Nat. Phys. 5 115 (2009)] that the collective excitation of two Rydberg atoms was observed, we provide an elaborate theoretical study for the dynamical behavior of two-atom Rabi oscillations. In the large-intermediate-detuning case, the two-photon Rabi oscillation is found to be significantly affected by the strength of the interatomic van der Waals interaction. With a careful comparison of the exact numbers and values of the oscillation frequency, we propose a new way to determine the strength of excitation blockade, well agreeing with the previous universal criterion for full, partial and none blockade regions. In the small-intermediate-detuning case we find a blockade-like effect, but the collective enhancement factor is smaller than $\sqrt{2}$ due to the quantum interference of double optical transitions involving the intermediate state. Moreover, a fast two-photon Rabi oscillation in $ns$ timescale is manifested by employing intense lasers with an intensity of $\sim$MW/cm$^2$, offering a possibility of ultrafast control of quantum dynamics with Rydberg atoms.