Efficient numerical simulation of microwave-optical quantum transducers

For realization of quantum network, one of promising options is to convert microwave photon qubits, which are used in local superconducting processors, into optical photon qubits, which travel in the optical fibers connecting the remote processors. While devices so called quantum transducers will enable us such a conversion, their development is challenging since each of them is a hybrid system composed of a superconducting circuit, a mechanical resonator, a solid-state qubit, an optical cavity etc. To design a transducer, we need to have a detailed numerical simulation for the conversion process, such as the dependence of the output fields on the pulse shape of the input fields, the power spectrum, and coherent conversion rates. In our work, we have simulation for the above properties on two devices, one with an optomechanical crystal and the other with a diamond optomechanical crystal with a color center. We evaluate the power spectrum with a pulsed input by one-time correlator of an auxiliary resonator operator, which greatly reduces the computational cost, since standard methods require the evaluation of two-time correlators.