论文标题
倒塌点的两光鼠狂犬模型的结合状态
Bound states of two-photon Rabi model at the collapse point
论文作者
论文摘要
本文提供了证明在崩溃点上两光子量子兔模型的新型结合状态的证明。两光鼠模型的模型不仅有趣，这不仅是因为其在非线性光 - 摩擦相互作用中的重要作用，而且还因为它展示了称为“光谱崩溃”的多能级退化过程。两光子歼灭和创建操作员的挤压属性是这种现象的起源，该现象是对没有能量的$ω_0$的精心研究的。但是，许多数值研究指出，在存在$ω_0$的情况下，存在一些低级隔离状态，而其他高能状态却崩溃至$ e = - \fracΩ{2} $，这被称为光谱崩溃不完全。从真实空间中的特征值方程式中，在塌陷点上得出了与Schrodinger方程相似的一对二阶微分方程。这些微分方程为$ e = - \ e = - \fracΩ{2} $存在的存在提供了解释，并存在旋转缝隙$ω_0$的存在，以及更好地生成这些绑定状态的数值方法。
This paper presents a proof of the existence of novel bound states of the two-photon quantum Rabi model at the collapse point. The two-photon Rabi model is interesting not only for its important role on non-linear light-matter interaction, but also for the exhibition of many-energy-levels degenerating process called the "spectral collapse". The squeezing property of the two-photon annihilation and creation operators is the origin for this phenomenon which is well studied without the energy-slitting term $ω_0$. However, many numerical studies have pointed out that with the presence of $ω_0$ , some low-level isolated states exist while other high energy states collapse to $E=-\fracω{2}$, which known as incomplete spectral collapse. From the eigenvalue equation in real space, pair of second order differential equations, which are similarly to the Schrodinger equation, are derived at the collapse point. These differential equations provide explanation to the existence of isolated bound states below $E=-\fracω{2}$ with the presence of the spin slitting $ω_0$ and better numerical method to generate those bound states.
