Application of polaron picture in the two-qubit quantum Rabi model

Abstract: The polaron picture is employed to investigate and elucidate the physics of the two-qubit quantum Rabi model, which describes two identical qubits coupled to a common harmonic oscillator. This approach enables us to obtain the ground-state energy and some other simpler physical observables with high accuracy in all regimes of the coupling strengths $g$, while there is no constraint to the ration of tunneling frequency $\Omega$ and field frequency $\omega$, which is not simultaneously possible using previous methods. Besides, we also discover a new phenomenon which is not present in the one-qubit Rabi model: with the increase of coupling strength $g$, there is a transition of the ground state of the system from a multipolaron state to a bipolaron state. However, the tunneling frequency $\Omega$ counteracts this process. Specifically, when tunneling frequency $\Omega=0$, the system always stays in the bipolaron state.