Dark-like states for the multi-qubit and multi-photon Rabi models

There are special solutions, the well-known dark states, to the even-qubit Dicke models, which are the products of two-qubit singlets and a Fock state, where the qubits are decoupled from the photon field. These spin singlets can be used to store quantum correlations since they preserve entanglement even under dissipation, driving and dipole-dipole interactions. One of the features for these 'dark states' is that their eigenenergies are independent of the qubit-photon coupling strength. Here we have obtained a novel kind of exceptional solution—'dark-like states' for the multi-qubit and multi-photon Rabi models, whose eigenenergies are also constant in the whole coupling regime. But unlike the 'dark states', the qubits and photon field are coupled. Furthermore, the photon numbers are bounded from above commonly at 1, which is different from the one-qubit case. The existence conditions of these exceptional solutions are simpler than the exact isolated solutions, and may be fine tuned in experiments. While solutions to the single-qubit and multi-photon Rabi model exist only if the photon number $M⩽2$ and the coupling strength is below a certain critical value, the dark-like eigenstates for the multi-qubit and multi-photon Rabi model exist regardless of these constraints. In view of these properties of the dark-like states, they may find similar applications as 'dark states' in quantum information. (paper)