标题： 光子-磁振子晶体的非线性视角下的纠缠特性 显示英文标题

标题： Entanglement properties of photon-magnon crystal from nonlinear perspective

摘要： 量化两个连续玻色模之间的纠缠，例如自旋波和光子，并不容易。 通过量子朗之万方程计算的对数负性会受到热噪声的影响。 然而，这种方法需要进一步的近似。 一般非线性系统的相空间包含拓扑不同的区域，稳态可能对应于不同类型的固定点，如鞍点、稳定或不稳定螺旋点以及节点。 在本工作中，我们提出了一种新的方法。 即，我们推导出了完整的非线性方程组，其中包括自旋波和光子数算符及相位的方程。 我们表明，不仅数算符，相位对于探索固定点的特性以及自旋波-光子纠缠也很重要。 我们表明，非线性微分方程的定性理论方法也适用于光子-自旋波纠缠问题。 我们的主要发现是，纠缠在鞍点区域内不成立。 另一方面，纠缠的最大值对应于稳定节点和稳定螺旋区域之间的边界附近区域。 我们的方法非常普遍。 然而，我们针对一个特定系统进行了计算：基于钇铁石榴石（YIG）薄膜的光子-自旋波晶体，该薄膜上钻有周期性的空气孔。 我们的兴趣集中在特定波长和频率的自旋波，这些自旋波对应于自旋波凝聚态。 这些自旋波与相同频率的光子强烈耦合。 我们详细讨论了源于磁电耦合和有效Dzyaloshinskii-Moriya相互作用的自旋波和光子之间的相互作用。 我们表明，这种相互作用负责系统中稳健的光子-自旋波纠缠。 显示英文摘要

摘要： Quantifying the entanglement between two continuous bosonic modes, such as magnons and photons, is not trivial. The logarithmic negativity, calculated through the quantum Langevin equations is subjected to thermal noise. However this method requires further approximation. The phase space of a generic nonlinear system contains topologically different regions, and the steady state may correspond to the different types of fixed points, such as Saddle Points, Stable or unstable Spirals, and Nodes. In the present work, we propose a new procedure. Namely, we derived the complete set of nonlinear equations, which includes equations for the magnon and photon number operators and phases. We show that not only number operators but also phases are important for exploring the character of the fixed point, and magnon-photon entanglement. We showed that methods of the qualitative theory of nonlinear differential equations are also relevant for photon-magnon entanglement problems. Our main finding is that entanglement is not defined in the Saddle Point region. On the other hand, the maximum of the entanglement corresponds to the region near the border between the Stable node and Stable spiral regions. Our approach is quite general. However, we did calculations for a particular system: photon-magnon crystal based on the yttrium iron garnet (YIG) film with the periodic air holes drilled in the film. Our interest focuses on magnons with a particular wavelength and frequency corresponding to the magnon condensate. Those magnons couple strongly with the photons of similar frequency. We discuss in detail the interaction between magnons and photons originating from the magneto-electric coupling and the effective Dzyaloshinskii-Moriya interaction. We show that this interaction is responsible for the robust photon-magnon entanglement in the system.