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In this work, we propose a method to investigate controllable qubit-resonatorinteractions in a Dicke model with driven biased term. The nonlinearity ofspectrum, which can be induced by qubit-resonator interactions, plays animportant role in such controllable interactions. To gain insight intomechanism of the nonlinearity, we perform a unitary transformation to theHamiltonian. The results show that the nonlinearity of the transformedHamiltonian depends on the qubit-resonator coupling strength. The general formsof the effective Hamiltonians are discussed in detail based on the frequencymodulation approach. The dynamical evolution can be switched on and off byadjusting the modulation parameters. By utilizing such controllableinteractions, we discuss the creation of Dicke states and arbitrarysuperposition of Dicke states. We also consider the nonlinearity of energylevel for the limit of large qubit numbers. In the thermodynamics limit, thekerr type nonlinearity is induced from "magnon"-resonator coupling, and theselective preparation of "magnon" Fock states can be studied under "magnon"scenario.

Switchable selective interactions in a Dicke Model with Driven Biased term