A scheme is proposed to explore the absorption and susceptibility of hybrid quantum systems comprising superconducting qubits and two mechanical resonators.The results show that the transparency based on mechanically induced coherent population oscillation (MICPO) can be tuned by the Rabi frequency and decay rate of the mechanical resonator.We also demonstrate that the coupling strength between the two mechanical resonators can be detected by measuring the distance between two peaks in the probe spectrum.We also propose a new scheme for measuring the frequency of mechanical resonators.This study is of great significance in the fields of precision measurement and quantum information processing.
Mechanical systems have emerged as a compelling platform for applications in quantum information, leveraging advances in the control of phonons, the quanta of mechanical vibrations. Experiments have demonstrated the control and measurement of phonon states in mechanical resonators, and while dual-resonator entanglement has been demonstrated, more complex entangled states remain a challenge. Here, we demonstrate rapid multi-phonon entanglement generation and subsequent tomographic analysis, using a scalable platform comprising two surface acoustic wave resonators on separate substrates, each connected to a superconducting qubit. We synthesize a mechanical Bell state with a fidelity of
F=0.872±0.002 , and a multi-phonon entangled N = 2 N00N state with a fidelity of
F=0.748±0.008 . The compact, modular, and scalable platform we demonstrate will enable further advances in the quantum control of complex mechanical systems. Recent advancements have enabled quantum control and measurement of mechanical resonators. Here the authors demonstrate quantum entanglement between two mechanical resonators on separate substrates by sharing one and two quanta of energy, followed by quantum measurement of these entangled states.