A hybrid circuit QED platform for quantum control and measurement of mechanical systems

We aim to build a hybrid quantum platform combining circuit optomechanics with circuit QED to leverage their respective strengths to prepare, store, and measure quantum states. Low frequency mechanical resonators show promise for quantum memory, demonstrating long lifetimes and high linearity, however their quantum behavior has been mostly explored with Gaussian states. Circuit QED systems have demonstrated universal control and high-fidelity measurement of bosonic modes. In this work we couple a microwave optomechanical circuit to a circuit QED system using a SNAIL coupler. The mechanical circuits consists of a compliant mechanical membrane (15 MHz) that forms one of the plates of an LC resonator (4GHz); the circuit QED contains a high Q storage mode (5GHz) coupled to a transmon qubit (3GHz) and associated readout resonator (8GHz). Both the LC resonator and the storage mode have small participation in the SNAIL. At the appropriate bias point, we can enable a beamsplitter interaction between the storage and LC using a third order nonlinearity without inducing a Kerr shift that would preclude strong pump powers required for optomechanical interactions. This allows us to use the transmon qubit to prepare bosonic codewords in the storage mode and transfer them to the LC resonator and finally to the mechanical oscillator. Ideally, this hybrid quantum platform extends the ability to prepare and tomographically verify arbitrary states to low-frequency mechanical systems, while simultaneously imbuing circuit QED with novel sensing, storage and transduction capabilities.