Heralded Scheme for Entangling Microwave-optical Modes in Cavity Piezo-optomechanics*

Quantum state transfer between microwave and optical frequencies is important in the development of modular quantum computation. Most schemes to realize such a hybrid interface are based on direct quantum transduction, which, nevertheless, has to full stringent requirements such as high conversion efficiency and low added noise. Despite all the recent remarkable efforts, in practice, building a direct microwave-optical quantum transducer still remains a challenge. A possible way out is to generate entanglement between the two modes and use it as a resource for microwave-optical modes transfer through teleportation. In this work, we propose a heralded scheme to entangle microwave and optical modes via parametric down conversion in a generic cavity piezo-optomechanical system. By post-selecting a two-mode squeezed vacuum state, entangled microwave-optical photon pairs can be generated. The entanglement is verified by the Bell inequality violation for a wide range of feasible parameters, showing the potential of the entangled source for realizing quantum state transfer between microwave and optical frequencies. We will analyze the impact of thermal noises and dark counts on the entanglement verification.