In-phase and anti-phase entanglement dynamics of Rydberg atomic pairs

We study the correlated evolutions of two far-spaced Rydberg atomic pairs with different resonant frequencies, interacting via van der Waals (vdW) potentials and driven by a common laser field. They are found to exhibit in-phase (anti-phase) beating dynamics characterized by identical (complementary) intra-pair entanglements under a specific condition in regard of inter-pair vdW potentials and driving field detunings. This occurs when each atomic pair just oscillates between its ground state and symmetric entangled state because its doubly excited state and asymmetric entangled state are forbidden due to rigid dipole blockade and perfect destructive interference, respectively. More importantly, optimal inter-pair overall entanglement can be attained at each beating node corresponding to semi-optimal intra-pair entanglements, and inevitable dissipation processes just result in a slow decay of intra-pair and inter-pair entanglements yet without destroying in-phase and anti-phase beating dynamics.