We show that highly confined superfluid films are extremely nonlinear mechanical resonators, offering the prospect to realize a mechanical qubit. Specifically, we consider third-sound surface waves, with nonlinearities introduced by the van der Waals interaction with the substrate. Confining these waves to a disk, we derive analytic expressions for the cubic and quartic nonlinearities and determine the resonance frequency shifts they introduce. We predict single-phonon shifts that are three orders of magnitude larger than in current state-of-the-art nonlinear resonators. Combined with the exquisitely low intrinsic dissipation of superfluid helium and the strongly suppressed acoustic radiation loss in phononic crystal cavities, we predict that this could allow blockade interactions between phonons as well as two-level-system-like behavior. Our work provides a pathway towards extreme mechanical nonlinearities, and towards quantum devices that use mechanical resonators as qubits.

我们表明，高度受限的超流体薄膜是极其非线性的机械谐振器，为实现机械量子位提供了前景。具体而言，我们考虑第三声表面波，其范德华力与基底相互作用会引入非线性。将这些波限制在磁盘中，我们导出三次和四次非线性的解析表达式，并确定它们引入的共振频率偏移。我们预测单声子频移比当前最新的非线性谐振器大三个数量级。结合超流氦的极低的固有耗散以及声子晶体腔中强烈抑制的声辐射损失，我们预测这可能会允许声子之间的相互作用以及类似两级系统的行为。