Externally controlled Lotka-Volterra dynamics in a linearly polarized polariton fluid.
Externally controlled Lotka-Volterra dynamics in a linearly polarized polariton fluid.
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DOI：
10.1103/physreve.101.012207
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发表时间：
2019-03
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影响因子：
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通讯作者：
Matthias Pukrop;S. Schumacher
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文献类型：
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作者：
Matthias Pukrop;S. Schumacher
横向斑图的自发形成普遍存在于各种非线性动力学系统中。特别感兴趣的一个方面是对这种模式的主动控制。在非线性光学系统中，这可以用于具有晶体管性能的全光开关，例如，在平面量子阱半导体微腔中用极化激元实现。在这里，我们专注于一个特定的配置，它利用了相互作用的光驱动极化激元系统中的复杂的偏振依赖关系。除了详细的耦合光场激子动力学的数值模拟，在本文中，我们专注于推导一个简化的人口竞争模型，从非线性动力学系统的角度详细了解潜在的机制。我们表明，这样的模型采取的形式，两个竞争的人口明确包括一个源项，使外部控制的广义Lotka-Volterra系统。我们全面分析了空间各向异性和外部控制强度所覆盖的参数空间中定态的存在性和稳定性。我们还构建了非平凡区域的相边界和新兴的分叉的特点。人口竞争模型再现了在相当复杂的半导体系统的全数值模拟中观察到的开关的所有关键特征，同时对于完全的分析理解来说足够简单。
Spontaneous formation of transverse patterns is ubiquitous in nonlinear dynamical systems of all kinds. An aspect of particular interest is the active control of such patterns. In nonlinear optical systems this can be used for all-optical switching with transistorlike performance, for example, realized with polaritons in a planar quantum-well semiconductor microcavity. Here we focus on a specific configuration which takes advantage of the intricate polarization dependencies in the interacting optically driven polariton system. Besides detailed numerical simulations of the coupled light-field exciton dynamics, in the present paper we focus on the derivation of a simplified population competition model giving detailed insight into the underlying mechanisms from a nonlinear dynamical systems perspective. We show that such a model takes the form of a generalized Lotka-Volterra system for two competing populations explicitly including a source term that enables external control. We present a comprehensive analysis of both the existence and stability of stationary states in the parameter space spanned by spatial anisotropy and external control strength. We also construct phase boundaries in nontrivial regions and characterize emerging bifurcations. The population competition model reproduces all key features of the switching observed in full numerical simulations of the rather complex semiconductor system and at the same time is simple enough for a fully analytical understanding.