Strong interaction between long-distance cantilevers via squeezing-induced quantum criticality and macroscopic entanglement generation

Strong long-range coupling between distant cantilevers is vital to cantilever-based quantum information processing. Here, we present an effective approach for establishing strong coupling between two distant cantilevers and generating the corresponding entanglement by utilizing phonon-squeezing-induced quantum criticality, where the phonon squeezing is achieved through frequency-doubling electrical regulation of the spring constant. Our system comprises three cantilever mechanical resonators connected in series by voltage, with the middle cantilever modulated by voltage and coupled to spin qubits. With current experimentally accessible parameters, by exploiting the combined effects of phonon squeezing and quantum criticality, we can significantly enhance the coupling strength between the polariton and the cantilever mechanical resonator by two or more orders of magnitude, all while maintaining a constant connection voltage. Similar to the Raman process, the polariton is virtually excited under conditions of large detuning, enabling indirect strong coupling between the two spatially separated cantilever mechanical resonators. We find that even if the distance between the cantilever resonators is increased by more than two orders of magnitude, the coupling remains strong with the connection voltage unchanged. On this basis, we demonstrate the generation of entanglement between two macroscopic cantilevers separated by long distances and clearly show through the calculations that the system decay has a minimal effect on quantum entanglement for a range of parameters. Apart from that, we assess the feasibility of the proposed method utilizing currently available technology. The present approach is expected to offer immunity to the high energy consumption and noise associated with elevated voltages, paving the way for quantum information and computation with cantilever mechanical resonator architecture.