Greilich Alex, Kopteva Nataliia E, Korenev Vladimir L, Haude Philipp A, Bayer Manfred
Experimentelle Physik 2, Technische Universität Dortmund, Dortmund, Germany.
Ioffe Institute, St. Petersburg, Russia.
Nat Commun. 2025 Mar 26;16(1):2936. doi: 10.1038/s41467-025-58400-6.
The coupled electron-nuclear spin system in an InGaAs semiconductor as testbed of nonlinear dynamics can develop auto-oscillations, resembling time-crystalline behavior, when continuously excited by a circularly polarized laser. We expose this system to deviations from continuous driving by periodic modulation of the excitation polarization, revealing a plethora of nonlinear phenomena that depend on modulation frequency and depth. We find ranges in which the system's oscillations are entrained with the modulation frequency. The width of these ranges depends on the polarization modulation depth, resulting in an Arnold tongue pattern. Outside the tongue, the system shows a variety of fractional subharmonic responses connected through bifurcation jets when varying the modulation frequency. Here, each branch in the frequency spectrum forms a devil's staircase. When an entrainment range is approached by going through an increasing order of bifurcations, chaotic behavior emerges. These findings can be described by an advanced model of the periodically pumped electron-nuclear spin system. We discuss the connection of the obtained results to different phases of time matter.
作为非线性动力学测试平台的InGaAs半导体中的耦合电子 - 核自旋系统，在受到圆偏振激光连续激发时，会产生类似于时间晶体行为的自振荡。我们通过对激发偏振进行周期性调制，使该系统偏离连续驱动，从而揭示了大量依赖于调制频率和深度的非线性现象。我们发现了系统振荡与调制频率同步的范围。这些范围的宽度取决于偏振调制深度，从而形成阿诺德舌形图。在舌形图之外，当改变调制频率时，系统会表现出通过分岔流连接的各种分数次谐波响应。在这里，频谱中的每个分支都形成一个魔鬼阶梯。当通过增加分岔顺序接近一个同步范围时，会出现混沌行为。这些发现可以用周期性泵浦电子 - 核自旋系统的高级模型来描述。我们讨论了所得结果与时间物质不同相的联系。
