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Quantum Acoustics with Tunable Nonlinearity in the Superstrong Coupling Regime

Marco Scigliuzzo1,2,3,*, Léo Peyruchat4,1,*, Riccardo Maria Marabini4,1, Carla Becker4,1, Vincent Jouanny4,1, Per Delsing3,†, and Pasquale Scarlino4,1,‡

  • *These two authors contributed equally.
  • †Contact author: per.delsing@chalmers.se
  • ‡Contact author: pasquale.scarlino@epfl.ch
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PRX Quantum 7, 010359 – Published 24 March, 2026

DOI: https://doi.org/10.1103/rk3m-dnwp

Abstract

Precise control of mechanical modes in the quantum regime is a key resource for quantum technologies, offering promising pathways for quantum sensing with macroscopic systems and scalable architectures for quantum simulation. In this work, we realize a multimode mechanical cavity coupled to a superconducting Kerr resonator, which induces nonlinearity in the mechanical modes. The Kerr mode is realized by a flux-tunable superconducting quantum interference device (SQUID) array resonator, while the mechanical modes are implemented by a surface acoustic wave cavity. Both mechanical and electromagnetic modes are individually addressable via dedicated measurement lines, enabling full spectroscopic characterization. We introduce a straightforward protocol to measure the SQUID array resonator’s participation ratio in the hybrid acoustic modes, quantifying the degree of hybridization. The participation ratio reveals that our device operates at the onset of the multimode coupling regime, where multiple acoustic modes simultaneously interact with the nonlinear superconducting element. Furthermore, this platform allows controllable Kerr-type nonlinearities in multiple acoustic modes, with the participation ratio serving as the key parameter determining both the dissipation rates and nonlinear strengths of these hybridized modes. Close to the resonant regime, we measure a cross-Kerr interaction between seven pairs of mechanical modes, which is controllable via the SQUID array resonator detuning. Finally, we apply a two-photon parametric drive to the SQUID array resonator and observe the resulting parametric down-conversion and metastable state switching in a mechanical mode. These results establish a platform for engineering nonlinear multimode mechanical interactions, offering potential for future integration with superconducting qubits and implementation of multiple mechanical qubits.

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Popular Summary

Confined mechanical vibrations in engineered structures underpin a wide range of technologies, from frequency references to signal processing. In the quantum regime, these vibrations, called phonons, become powerful resources for quantum science, offering exceptional sensitivity to weak forces, acceleration, and even gravitational effects. Unlocking this potential requires not only detecting phonons but also engineering controlled interactions between them.

Phonons are generally linear excitations and therefore do not naturally interact with one another. Interactions can be engineered; however, by hybridizing mechanical modes with a nonlinear microwave resonator, allowing phonons to inherit effective self- and cross-Kerr nonlinearities. In such hybrid systems, the key quantity governing both dissipation and interaction strength is the participation ratio, which quantifies the extent to which each mechanical mode mixes with the nonlinear element. Despite its central importance, this parameter is often inferred from simulations rather than measured directly.

In this work, we couple a microwave Kerr resonator to multiple surface acoustic wave modes and experimentally extract their degree of hybridization. We show that even a small participation of the nonlinear resonator is sufficient to induce sizable mechanical nonlinearities. Using this approach, we directly measure cross-Kerr interactions between mechanical modes and observe bistability under a two-photon drive, a hallmark of dissipative nonlinear dynamics. Our results establish a general experimental framework for engineering and characterizing interacting phonons in hybrid quantum systems that can be used for exploring nonlinear and collective mechanical phenomena.

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PRX Quantum 7, 010359– Published 24 March, 2026
  • Received 24 June 2025
  • Revised 29 December 2025
  • Accepted 9 January 2026
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