Steady state entanglement between hybrid light-matter qubits

We study the case of two polaritonic qubits localized in two separate cavities coupled by a fiber/additional cavity. We show that surprisingly enough, even a coherent classical pump in the intermediate cavity/fiber can lead to the creation of entanglement between the two ends in the steady state. The stationary nature of this entanglement and its survival under dissipation opens possibilities for its production under realistic laboratory conditions. To facilitate the verification of the entanglement in an experiment we also construct the relevant entanglement witness measurable by accessing only a few local variables of each polaritonic qubit.