Ultrafast and deterministic generation of Bell states in the ultrastrong coupling regime

We have found the special dark state solutions of the anisotropic two-qubit quantum Rabi model (QRM), which has at most one photon, and constant eigenenergy in the whole coupling regime. Accordingly, we propose a scheme to deterministically generate two kinds of the two-qubit Bell states through adiabatic evolution along the dark states. With the assistance of the Stark shift, the generation time can be reduced to subnanosecond scales, proportional to the reverse of the resonator frequency, with fidelity reaching 99%. Furthermore, the other two kinds of Bell states can also be ultrafast generated.