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Dark-state polaritons (DSPs) based on the effect of electromagneticallyinduced transparency are bosonic quasiparticles, representing thesuperpositions of photons and atomic ground-state coherences. It has beenproposed that stationary DSPs are governed by the equation of motion closelysimilar to the Schr\"{o}dinger equation and can be employed to achieveBose-Einstein condensation (BEC) with transition temperature orders ofmagnitude higher than that of the atomic BEC. The stationary-DSP BEC is athree-dimensional system and has a far longer lifetime than theexciton-polariton BEC. In this work, we experimentally demonstrated thestationary DSP dressed by the Rydberg-state dipole-dipole interaction (DDI).The DDI-induced phase shift of the stationary DSP was systematically studied.Notably, the experimental data are consistent with the theoretical predictions.The phase shift can be viewed as a consequence of elastic collisions. In termsof thermalization to achieve BEC, the $\mu$m$^2$-size interaction cross-sectionof the DDI can produce a sufficient elastic collision rate for the stationaryDSPs. This work makes a substantial advancement toward the realization of thestationary-DSP BEC.

Experimental Demonstration of Stationary Dark-State Polaritons Dressed by Dipole-Dipole Interaction