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Entanglement dynamics of the ultra-strong coupling three-qubit Dicke model

We give an analytical description of the dynamics of the three-qubit Dicke model using the adiabatic approximation in the parameter regime where the qubits transition frequencies are far off-resonance with the field frequency and the interaction strengths reach the ultra-strong coupling regimes. Qualitative differences arise when comparing to the single- and two-qubit systems - simple analytic formulas show that three revival sequences produce a three-frequency beat note in the time evolution of the population. We find an explicit way to estimate the dynamics for the qubit-field and qubit-qubit entanglement inside the three-qubit system in the ultra strong coupling regime, and the resistance to the sudden death proves the robustness of the GHZ state.