Entangling two Dicke states in a periodic modulated quantum system

We propose a theoretical approach for entangling two Dicke states in a periodic modulated quantum system. By considering two qubit ensembles that are nonuniformly coupled to a common resonator, we can derive an effective Hamiltonian whose energy levels depend nonlinearly on the excitation number of each qubit ensemble. More simplified effective Hamiltonian can be obtained by selecting appropriate driving parameters and initial state. Based on the dynamic evolution of the effective Hamiltonian, we can selectively achieve Dicke state transitions and generate entangled Dicke states controllably. For a special case, we can obtain ensemble-ensemble entangled states by performing a projective even-odd cat measurement. By implementing Gaussian soft temporal modulation, we can effectively suppress off-resonant contributions in the interaction and enhance the fidelity of target states. Furthermore, by utilizing the Holstein-Primakoff transformation, we study the resonator-ensemble coupling system in the thermodynamic limit and investigate the generation of entangled magnon states. Additionally, we propose a scheme of creating magnon NOON states through frequency modulation and study the influence of decoherence on the fidelity of target states.