We explore the dissipative dynamics of nonlinearly driven oscillator systems tuned to resonances where multiple excitations are generated. Such systems are readily realised in circuit QED systems combining Josephson junctions with a microwave cavity and a drive achieved either through flux or voltage bias. For resonances involving three or more photons the system undergoes a sequence of two closely spaced dynamical transitions (the first one discontinuous and the second continuous) as the driving is increased leading to steady states that form complex periodic structures in phase space. In the vicinity of the transitions the system displays interesting bistable behaviour: we find that coherent effects can lead to surprising oscillations in the weight of the different dynamical states in the steady state of the system with increasing drive. We show that the dynamics is well-described by a simple effective rate model with transitions between states localised at different points in the phase space crystal. The oscillations in the weights of the dynamical states is reflected in corresponding oscillations in a time-scale that describes transitions between the states.

我们探索了非线性驱动振荡器系统的耗散动力学，该系统调谐到产生多个激励的共振。这种系统很容易在电路 QED 系统中实现，该系统将约瑟夫森结与微波腔和通过通量或电压偏置实现的驱动相结合。对于涉及三个或更多光子的共振，随着驱动的增加导致在相空间中形成复杂周期结构的稳态，系统经历一系列两个紧密间隔的动态跃迁（第一个不连续和第二个连续）。在跃迁附近，系统显示出有趣的双稳态行为：我们发现，随着驱动力的增加，相干效应会导致系统稳态下不同动力学状态的权重发生惊人的振荡。我们表明，动力学可以通过简单的有效速率模型很好地描述，该模型具有位于相空间晶体中不同点的状态之间的转变。动态状态权重的振荡反映在描述状态之间转换的时间尺度中的相应振荡中。