We investigate the coherent coupling of metamaterial resonators with hydrogen-like boron acceptors in Si at cryogenic temperatures. When the resonance frequency of the metamaterial, chosen to be in the range 7-9 THz, superimposes the transition frequency from the ground state of the acceptor to an excited state, Rabi splitting as large as 0.4 THz is observed. The coherent coupling shows a feature of cooperative interaction, where the Rabi splitting is proportional to the square root of the density of the acceptors. Our experiments may help to open a possible route for the investigation of quantum information processes employing strong coupling of dopants in cavities.