Quantum non-demolition measurement of single phonon state with nitrogen-vacancy centers ensemble and superconducting qubit

We propose a scheme to realize the quantum non-demolition single phonon detection and emission based on the interaction between the NV ensemble and the superconducting flux qubit. The resonant frequency of the flux qubit will change with the NVE absorbing a single phonon, then we can detect the single phonon state through measuring the frequency shift of the flux qubit. The fidelity of the absorbing process can reach a much high value. After the detection process, the NVE can emit the absorbed phonon as we apply a driving pulse which is in reverse to the absorbing process. The overlap between the input and the output phonon shapes can reach 98.57%. The scheme can be realized under the realistic experimental condition.