Mechanical degrees of freedom are natural candidates for continuous-variable quantum information processing and bosonic quantum simulations. However, these applications require the engineering of squeezing and nonlinearities in the quantum regime. Here we demonstrate squeezing below the zero-point fluctuations of a gigahertz-frequency mechanical resonator coupled to a superconducting qubit. This is achieved by parametrically driving the qubit, which results in an effective two-phonon drive. In addition, we show that the resonator mode inherits a nonlinearity from the off-resonant coupling with the qubit, which can be tuned by controlling the detuning. We, thus, realize a mechanical squeezed Kerr oscillator, in which we demonstrate the preparation of non-Gaussian quantum states of motion with Wigner function negativities and high quantum Fisher information. This shows that our results can also have applications in quantum metrology and sensing.

机械自由度是连续可变量子信息处理和玻色子量子模拟的自然候选者。然而，这些应用需要量子态中的压缩和非线性工程。在这里，我们演示了将与超导量子位耦合的千兆赫频率机械谐振器压缩到零点波动以下。这是通过参数化驱动量子位来实现的，从而产生有效的双声子驱动。此外，我们还表明，谐振器模式继承了与量子位的非谐振耦合的非线性，可以通过控制失谐来调节非线性。因此，我们实现了机械压缩克尔振荡器，其中我们演示了具有维格纳函数负性和高量子费希尔信息的非高斯量子运动态的制备。这表明我们的结果也可以在量子计量和传感领域得到应用。