A parametric coupling scheme for mitigating piezoelectric loss in quantum acoustics devices*

Quantum states of mechanical motion offer the potential to realize long lived multimodal quantum memories as well as quantum transduction between disparate quantum systems.  Coupling this motion to superconducting qubits through piezoelectricity provides the toolkit of circuit quantum electrodynamics for quantum control over phonons.  However, this interface is also a source of loss due to radiation into spurious phonon modes.  This results in superconducting qubit lifetimes around two orders of magnitude smaller than those on the best dielectrics.  Here we present a 3D cavity architecture to mitigate the deleterious effect of this extra loss by removing the qubit entirely from the piezoelectric substrate and instead parametrically coupling the qubit to the acoustic modes utilizing a 3D superconducting nonlinear asymmetric inductive element (SNAIL).  This design allocates the loss primarily to the SNAIL coupler, and so operating with small qubit participation in this SNAIL mode will allow for longer qubit lifetimes.  We demonstrate strong coupling between our SNAIL coupler and the longitudinal modes of a surface acoustic wave resonator and characterize its 3-wave mixing nonlinearity.