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We investigate the coherent manipulation of interacting Rydberg atoms placedinside a high-finesse optical cavity for the deterministic preparation ofstrongly coupled light-matter systems. We consider a four-level diamond schemewith one common Rydberg level for N interacting atoms. One side of the diamondis used to excite the atoms into a collective `superatom' Rydberg state usingeither {\pi}-pulses or stimulated Raman adiabatic passage (STIRAP) pulses. Theupper transition on the other side of the diamond is used to transfer thecollective state to one that is coupled to a field mode of an optical cavity.Due to the strong interaction between the atoms in the Rydberg level, theRydberg blockade mechanism plays a key role in the deterministic quantum statesynthesis of the atoms in the cavity. We use numerical simulation to show thatnon-classical states of light can be generated and that the state that iscoupled to the cavity field is a collective one. We also investigate howdifferent decay mechanisms affect this interacting many-body system. We alsoanalyze our system in the case of two Rydberg excitations within the blockadevolume. The simulations are carried out with parameters corresponding torealizable high-finesse optical cavities and alkali atoms like rubidium.

Collective state synthesis in an optical cavity using Rydberg atom blockade