Cross-Kerr interaction enhanced coupling in a hybrid electromechanical device

Superconducting hybrid devices have emerged as a promising platform for the control of motional states of massive resonators. We report a hybrid electromechanical device consisting of a mechanical resonator coupled to a transmon qubit via the modulation of the Josephson inductance. The qubit readout is performed by coupling to a 3D-microwave cavity. In such a tri-partite system, a large coupling between the mechanical resonator and the microwave photons can be achieved when qubit frequency is tuned close to the cavity mode. However, in the dispersive limit, the direct coupling between the cavity mode and the mechanical resonator can reduce significantly. Here we experimentally show that, in the dispersive limit, the optomechanical coupling can be increased by adding a weak drive near the qubit frequency. Such an enhancement in optomechanical coupling arises from the cross-Kerr interaction between the cavity and the qubit. Our theoretical modeling suggests that such a cross-Kerr interaction can be a valuable resource for the quantum control of the mechanical resonator.