Non-Gaussian macroscopic entanglement of motion in a hybrid electromechanical device

We propose a scheme for entangling the motion of two massive objects in a hybrid electromechanical architecture. The entanglement is generated due to the interaction of two mechanical oscillators with a mediating superconducting qubit. We show that the generated macroscopic entangled states are non-Gaussian and its lifetime is limited by coherence time of the qubit. The entanglement is attainable in a wide range of parameters with appropriate control of the qubit. We confirm performance of our scheme by numerically solving the quantum optical master equation including sources of noise. The effect of imperfections, such as asymmetries in the coupling rates as well as mechanical thermal noise are studied and shown how they affect the amount and lifetime of the entangled state. Due to the nonlinear nature of the qubit, the initial Gaussian state of mechanical resonators evolves into a quasi-stationary non-Gaussian state, which is essential for universal quantum information processing in continuous variable systems. This work, therefore, provides the first step towards a universal continuous variable quantum network.