In-phase and antiphase dynamics of Rydberg atoms with distinguishable resonances

We study the correlated evolutions of two Rydberg atoms, interacting via a van der Waals (vdW) potential V-6 and driven by a laser field of detunings Delta(1) and Delta(2). The two atoms may exhibit the in-phase dynamics with identical Rydberg populations or the antiphase dynamics with complementary Rydberg populations, depending on their initial states. For a moderate vdW potential far from the blockade regime, the in-phase or antiphase dynamics can be attained along two intersecting lines in the parameter space of Delta(1) and Delta(2) with an exact or approximate figure of merit, respectively. Note, in particular, that the exact in-phase dynamics is trivial because it requires identical detunings while the approximate in-phase, exact antiphase, and approximate antiphase dynamics are nontrivial because they require distinct detunings. The specific requirements on Delta(1) and Delta(2) for both in-phase and antiphase dynamics can be understood by considering the balanced transitions from two initially populated states to two initially empty states in the double-atom state basis.