Vibrationally coupled Rydberg atom-ion molecules

We study the occurrence of Rydberg atom-ion molecules (RAIMs) in a hybrid atom-ion system with an ion crystal trapped in a Paul trap coupled to Rydberg atoms on its either ends. To assess the feasibility of such a system, we perform a detailed Floquet analysis of the effect of the Paul trap's rf potential on the RAIMs and provide a qualitative analysis of the survival probability based on scaling laws. We conclude that the RAIM survives for sufficiently weak and low frequency traps. We then use this hybrid system and propose a scheme to utilise the common motional modes of the ion crystal to suppress (blockade) or enhance (anti-blockade) the probability of forming two RAIMs at the ends of the chain, replacing the typical blockade radius by the length of the ion crystal.