论文标题
非线性狂犬模型的统一方法
Unified approach to the nonlinear Rabi models
论文作者
论文摘要
提出了一种分析方法来研究两光子，两模式和强度依赖性的RABI模型。凭借SU（1,1）为代数，所有这些都可以用$ \ Mathcal {z} _2 $对称统一到同一哈密顿量。存在精确的孤立溶液，该解决方案位于不同奇偶群之间的级别交叉口，对应于具有有限尺寸的本征态。除了确切的孤立溶液之外，可以通过找到G功能的根来实现规则光谱。相应的本征态是无限的维度。值得注意的是，本征态的膨胀系数表现出指数衰减的行为。衰减速率随着耦合强度的增加而降低。当耦合强度趋向于光谱塌陷点$ g \ rightarrowω/ 2 $时，衰减速率趋于零，从而阻止了波函数的收敛性。这项工作铺平了一种分析非线性量子光学物质新物理学的方法。
An analytical approach is proposed to study the two-photon, two-mode and intensity-dependent Rabi models. By virtue of the su(1,1) Lie algebra, all of them can be unified to the same Hamiltonian with $\mathcal{Z}_2$ symmetry. There exist exact isolated solutions, which are located at the level crossings between different parities and correspond to eigenstates with finite dimension. Beyond the exact isolated solutions, the regular spectrum can be achieved by finding the roots of the G-function. The corresponding eigenstates are of infinite dimension. It is noteworthy that the expansion coefficients of the eigenstates present an exponential decay behavior. The decay rate decreases with increasing coupling strength. When the coupling strength tends to the spectral collapse point $g \rightarrow ω/ 2$, the decay rate tends to zero which prevents the convergence of the wave functions. This work paves a way for the analysis of novel physics in nonlinear quantum optics.
