参量激发引起的混沌：相空间对称性和光子关联
Chaos due to parametric excitation: phase space symmetry and photon correlations
摘要：
讨论了参数驱动的非线性克尔腔（PDNR）的相空间对称性耗散混沌和非经典统计。在这个系统中，振荡模式是在与外部高斯脉冲的训练相互作用下光子的简并下转换过程中产生的。对于混沌状态，我们证明，庞加莱截面显示一个奇异吸引子，以及谐振器模式轮廓图的维格纳函数显示在相空间中的双重对称性。我们发现，量子到经典的对应关系是强烈违反了一些混沌制度的PDNR。在考虑二阶关联函数的情况下，我们发现当系统过渡到混沌态时，导致压缩的光子关联将大大降低.因此，光子数相关性的观测允许提取关于混沌状态的信息。
英文摘要：
We discuss dissipative chaos showing symmetries in the phase space and nonclassical statistics for a parametrically driven nonlinear Kerr resonator (PDNR). In this system an oscillatory mode is created in the process of degenerate down-conversion of photons under interaction with a train of external Gaussian pulses. For chaotic regime we demonstrate, that the Poincaré section showing a strange attractor, as well as the resonator mode contour plots of the Wigner functions display two-fold symmetry in the phase space. We show that quantum-to-classical correspondence is strongly violated for some chaotic regimes of the PDNR. Considering the second-order correlation function we show that the high-level of photons correlation leading to squeezing in the regular regime strongly decreases if the system transits to the chaotic regime. Thus, observation of the photon-number correlation allows to extract information about the chaotic regime.
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