A multimode nonlinear resonator for quantum acoustics

Exploiting multiple modes in a quantum acoustic device could enable applications in quantum information in a hardware-minimal setup. Surface Acoustic Wave (SAW) resonators in the quantum regime support high Q-factors (>10^5) and dense mode spectra. We introduce a Kerr nonlinearity to a SAW resonator by integrating a SQUID (Superconducting QUantum Interference Device) into one of the Bragg reflectors. The SQUID inductance modulates the reflectivity of each unit cell in the mirror and hence the effective length of the resonator. Due to the narrow free spectral range, this gives rise to a cross-Kerr coupling between the more than 20 accessible modes. We attempt to exploit this nonlinear coupling to generate multimode non-classical states that could potentially provide a resource for quantum computation. Avenues towards quantum simulation using the coupled modes as lattice sites occupied by SAW phonons are further explored.