Branch-entangled polariton pairs in planar microcavities and photonic wires

A scheme is proposed for the generation of branch-entangled pairs of microcavity polaritons through spontaneous interbranch parametric scattering. Branch entanglement is achievable when there are two twin processes, where the role of signal and idler can be exchanged between two different polariton branches. Branch entanglement of polariton pairs can lead to the emission of frequency-entangled photon pairs out of the microcavity. In planar microcavities, the necessary phase-matching conditions are fulfilled for pumping of the upper polariton branch at an arbitrary in-plane wave vector. The important role of nonlinear losses due to pair scattering into high-momentum exciton states is evaluated. The results show that the lack of protection of the pump polaritons in the upper branch is critical. In photonic wires, branch entanglement of one-dimensional polaritons is achievable when the pump excites a lower polariton sub-branch at normal incidence, providing protection from the exciton reservoir.