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Summary form only given. The preparation of simple entangled quantum systems and the demonstration of their nonclassical properties has been a challenging goal since the early days of quantum mechanics and the famous Einstein Poldolsky Rosen (ERR) paper. Using circular Rydberg atoms strongly interacting with a zero or one-photon field stored in a microwave superconducting cavity, we have been able to prepare a new kind of EPR pair involving two entangled massive particles. The entanglement originates from the Rabi oscillation of a single excited atom emitting a photon in an initially empty cavity on a transition between two adjacent Rydberg levels.