Stationary and dynamical entanglements in microcavity exciton polaritons

We propose a scheme for generating genuinely tripartite entanglements in microcavity exciton polaritons comprised of an exciton, photon, and phonon modes. We search for robust stationary bipartite and tripartite entanglements by optimizing optomechanical parameters while revealing the mechanism for generating entangled states by non-Hermitian spectrum. Maximum photon-phonon and exciton-phonon bipartite entanglements appear at the cross points of real eigenvalues in the non-Hermitian spectrum, while photon-exciton bipartite entanglements and tripartite entanglements are related to the breaking of parity-time symmetry. We also demonstrate entanglement dynamics and discover entanglement oscillations, transformation, and sudden death. Entanglement transformation among different bipartite entanglements and entanglement sudden death can be effectively regulated by cavity-exciton detunings and exciton-photon-phonon couplings. Moreover, thermal noises should be degraded to generate robust stationary entanglements and maintain prolonged dynamical entanglements. Our results open up new possibilities for constructing exciton-photon-phonon tripartite entanglements, which may have potential applications in developing quantum computing and quantum information processing protocols based on macroscopic entangled states.