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

Abstract

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 ${\mathrm{\ensuremath{\Delta}}}_{1}$ and ${\mathrm{\ensuremath{\Delta}}}_{2}$. 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 ${\mathrm{\ensuremath{\Delta}}}_{1}$ and ${\mathrm{\ensuremath{\Delta}}}_{2}$ 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 ${\mathrm{\ensuremath{\Delta}}}_{1}$ and ${\mathrm{\ensuremath{\Delta}}}_{2}$ 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.