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Experimental realization of a quantum phase transition of polaritonic excitations

We report an experimental realization of the Jaynes-Cummings-Hubbard (JCH) model using the internal and radial phonon states of two trapped ions. An adiabatic transfer corresponding to a quantum phase transition from a localized insulator ground state to a delocalized superfluid (SF) ground state is demonstrated. The SF phase of polaritonic excitations characteristic of the interconnected Jaynes-Cummings (JC) system is experimentally explored, where a polaritonic excitation refers to a combination of an atomic excitation and a phonon interchanged via a JC coupling.