The resonant dipole-dipole interaction between highly excited Rydberg levels dominates the interaction of neutral atoms at short distances scaling as $1/r^3$. Here we take advantage of the combined effects of strong dipole-dipole interaction and multifrequency driving fields to propose one type of selective Rydberg pumping mechanism. In the computational basis of two atoms $\left\{\right|00\rangle ,|01\rangle ,|10\rangle ,|11\rangle \}$, this mechanism allows $|11\rangle$ to be resonantly pumped upwards to the single-excited Rydberg states while the transitions of the other three states are suppressed. From the perspective of mathematical form, we achieve an analogous Förster resonance for ground states of neutral atoms. The performance of this selective Rydberg pumping is evaluated using the definition of fidelity for a controlled-$Z$ gate, which manifests a characteristic robustness to the deviation of interatomic distance, fluctuation of Förster resonance defect, and spontaneous emission of double-excited Rydberg states. As applications of this mechanism, we discuss in detail the preparation of the maximally entangled symmetric state for two atoms via ground-state blockade, and the maximally entangled antisymmetric state via engineered spontaneous emission, within the state-of-the-art experiments, respectively.

• Received 26 June 2020
• Accepted 11 November 2020

DOI:https://doi.org/10.1103/PhysRevA.102.053118