Frequency entrainment of continuous-variable oscillators has to date been restrained to the weakly nonlinear regime. Here we overcome this bottleneck and extend frequency entrainment of quantum continuous-variable oscillators to arbitrary nonlinearities. The previously known steady state of such quantum oscillators in the weakly nonlinear regime (also known as a Stuart-Landau oscillator) is shown to emerge as a special case. Most importantly, the hallmark of strong nonlinearity—relaxation oscillations—is shown in quantum mechanics. Depending on the oscillator's nonlinearity, relaxation oscillations are found to occur via two distinct mechanisms in phase space.

中文翻译：

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量子力学中的弛豫振荡和频率夹带

迄今为止，连续可变振荡器的频率夹带已经被限制在弱非线性范围内。在这里，我们克服了这个瓶颈，并将量子连续变量振荡器的频率夹带扩展到任意非线性。这种量子振荡器在弱非线性状态下的先前已知稳态（也称为Stuart-Landau振荡器）被证明是一种特殊情况。最重要的是，量子力学显示出强非线性的特征-松弛振动。根据振荡器的非线性，发现弛豫振荡是通过相空间中的两种不同机制发生的。