It is an open question whether mechanical resonators can be made nonlinear with vibrations approaching the quantum ground state. This requires the engineering of a mechanical nonlinearity far beyond what has been realized so far. Here we discover a mechanism to boost the Duffing nonlinearity by coupling the vibrations of a nanotube resonator to single-electron tunnelling and by operating the system in the ultrastrong-coupling regime. We find that thermal vibrations become highly nonlinear when lowering the temperature. The average vibration amplitude at the lowest temperature is 13 times the zero-point motion, with approximately 42% of the thermal energy stored in the anharmonic part of the potential. Our work may enable the realization of mechanical Schrödinger cat states, mechanical qubits and quantum simulators emulating the electron–phonon coupling.

机械谐振器是否可以通过接近量子基态的振动制成非线性的，这是一个悬而未决的问题。这需要远远超出目前已经实现的机械非线性工程。在这里，我们发现了一种通过将纳米管谐振器的振动耦合到单电子隧穿并通过在超强耦合状态下操作系统来增强达芬非线性的机制。我们发现，当温度降低时，热振动会变得高度非线性。最低温度下的平均振幅是零点运动的13倍，约42%的热能储存在势能的非谐波部分。我们的工作可以实现机械薛定谔猫态，