Reduced Density Matrix and Quantum Correlation in Two-Qubit Quantum Rabi Model

In this work, we give an analytical derivation of the reduced density matrix between two qubits in a cavity field, which is described by the quantum Rabi model. Using the coherent state method and the generalized hypergeometric functions, we find a complete solution of the 4-by-4 reduced density matrix for each eigen energy by taking the partial trace over the cavity field states. Four kinds of measurements used to describe the quantum entanglement and quantum correlation between the two qubits, i.e., the concurrence, quantum discord, steerable weight, and robustness of coherence, are calculated for the ground state and excited states. For both the weak coupling ( $g\rightarrow 0$ ) and deep-strong coupling ( $g\rightarrow \infty $ ) regimes, quantum entanglement and quantum correlation between the two qubits are vanishing. An appropriate coupling in the deep strong coupling regime between the qubits and the cavity field is required if one wants to establish quantum entanglement between the qubits.