光学机械中通过例外点的频率锁定和可控混沌
Frequency locking and controllable chaos through exceptional point in optomechanics
摘要：
我们在由两个机械耦合的光机械腔（OMC）组成的系统中设计机械增益（损耗）。通过用蓝（红）失谐的激光驱动谐振器来控制增益（损耗）。我们预测分析存在多个例外点（EP），一种形式的退化的系统的特征值合并。在每个EP，发生相变，并且系统从弱耦合区切换到强耦合区，反之亦然。在弱耦合状态下，系统锁定在中间频率上，这是由EP处的聚结引起的。而在强耦合区，则会激发出两个或多个力学模态，这取决于系统参数。当两个机械模同时作用时，机械谐振器呈现拉比振荡，反之，在强耦合区，相互作用触发混沌。这种混沌是有界的EP，使其易于控制，通过调整这些退化。此外，这种混沌吸引子出现在低驱动功率，当耦合OMC都在蓝色边带驱动时发生的情况相比。这些工作开辟了有前途的途径，使用EP作为一种新的工具，研究集体现象（同步，锁定效应）在非线性系统，并控制混沌。
英文摘要：
We engineer mechanical gain (loss) in system formed by two optomechanical cavities (OMCs), that are mechanically coupled. The gain (loss) is controlled by driving the resonator with laser that is blue (red) detuned. We predict analytically the existence of multiple exceptional points (EPs), a form of degeneracy where the eigenvalues of the system coalesce. At each EP, phase transition occurs, and the system switches from weak to strong coupling regimes and vice versa. In the weak coupling regime, the system locks on an intermediate frequency, resulting from coalescence at the EP. In strong coupling regime, however, two or several mechanical modes are excited depending on system parameters. The mechanical resonators exhibit Rabi-oscillations when two mechanical modes are involved, otherwise the interaction triggers chaos in strong coupling regime. This chaos is bounded by EPs, making it easily controllable by tuning these degeneracies. Moreover, this chaotic attractor shows up for low driving power, compared to what happens when the coupled OMCs are both drived in blue sidebands. This works opens up promising avenues to use EPs as a new tool to study collective phenomena (synchronization, locking effects) in nonlinear systems, and to control chaos.
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