Coherence enhancement of Rydberg polaritons

Quantum nonlinear optics by Rydberg polaritons can enable single-photon transistor and switch, single-photon source, and deterministic quantum information processing. A major hindrance in this study is the fast motional decoherence. Here, we devise a scheme to significantly enhance the coherence of Rydberg polariton by letting the atoms {\it remember} their velocities, or, alternatively, by {\it changing} the phase of Rydberg polariton according to its storage time. After the Rydberg polariton is prepared with a Rydberg state $|r_1\rangle$, i.e., during the storage time, two laser fields induce a transition between $|r_1\rangle$ and a nearby Rydberg state $|r_2\rangle$ via a low-lying intermediate state $\lvert f\rangle$ which is largely detuned. In particular, we find that either a $2\pi\mathbb{N}$ protocol, a $\pi$-wait-$\pi$ protocol, or a wait-$\pi$ protocol, along with an appropriate choice of $\lvert f\rangle$ can lead to a phase-coherent Rydberg polariton upon its retrieval. Importantly, the coherent transition between $|r_1\rangle$ and $|r_2\rangle$ ensures that the Rydberg polariton can block the Rydberg excitation of nearby atoms as in usual applications of Rydberg polaritons. Numerics show that the theory can nearly completely eliminate the motional dephasing, leaving Rydberg-state decay as the only fundamental channel of decoherence. This sheds light on a broad application of Rydberg-mediated quantum nonlinear optics.