Solitonic behaviour in coupled multi atom-cavity systems

In view of current research effort on semiconducting photonic-crystal defect microcavities, we consider the dynamics of an array of coupled optical cavities, each containing an ensemble of qubits. By concentrating on the strong coupling regime, we analytically prove that the nonlinearity inherent in the dynamics of each ensemble coupled to the respective cavity field allows the formation of solitons. We further show how the use of the Holstein-Primakoff transformation and the large-detuning limit with the cavity allows one to recover the Bose-Hubbard model