Joint tomography and quantum entanglement of a pair of nanomechanical oscillators

The field of quantum acoustics combines the advantages of nanomechanical resonators with the established techniques of circuit QED to achieve quantum control of mechanical systems. These hybrid acoustic devices have been proposed as promising platforms for quantum random access memories and biased-error cat qubits [2-4], but current devices have not demonstrated control of multiple mechanical oscillators with a single qubit. In this talk, we present a small quantum acoustic processor used to synthesize and characterize quantum entanglement between two nanomechanical resonators [1]. The device is composed of two thin-film phononic crystal resonators coupled to a superconducting transmon qubit, which we use to manipulate the quantum states of the joint mechanical system. After preparing the mechanical resonators in a Bell-state, we perform full joint quantum state tomography using a non-demolition measurement where the qubit is dispersively coupled to both resonators simultaneously. The reconstructed quantum states for the joint mechanical system show good agreement with numerical simulations, suggesting that the measured state fidelities are limited by decoherence mechanisms in the mechanical resonators.