论文标题
基于高频扩展的扩展狂犬模型的浮quet分析
Floquet analysis of extended Rabi models based on high-frequency expansion
论文作者
论文摘要
扩展的量子狂犬模型为了解原子光相互作用的量子性质做出了重要贡献。我们将两种扩展的量子兔模型，各向异性兔模型和不对称的兔模型转化为旋转框架，并将它们视为定期驱动的量子系统。 The analytical solutions of the quasi-energy spectrum as well as the Floquet modes for both models are constructed by applying the Floquet theory and the high-frequency expansion, which is applied to the non-stroboscopic dynamics of physical observables such as atomic inversion, transverse magnetization, atom-field correlation, etc. For anisotropic Rabi model, the quasi energy fits well with the numerical results即使旋转波耦合在深度耦合方案中，如果与驾驶频率相比，反向旋转项足够小，则$ g \ simeq \hbarΩ$。当总兴奋数$ n $ $ n $ n+2 $的正面分支频谱线$ n+2 $时，准能量可能会发生相同平等的准能量交叉，而高频膨胀由于保存总的激发数量而无法预测这一点。此外，我们介绍了人口长期演变的分析和数值研究，并确定分析方法对于人群动态是可信的。对于不对称的RABI模型，我们发现打破总激发数的平均对称性的外部偏置场倾向于将上和下分支聚集成两个束，并且在第一个颞叶brillouin区域中引起的诱发差距显示出对偏置的二次依赖性。这两种模型都证明，通过浮雕理论在旋转框架中处理哈密顿量，在原子与光之间的相互作用研究中提供了一种替代工具。
The extended quantum Rabi models make a significant contribution to understand the quantum nature of the atom-light interaction. We transform two kinds of extended quantum Rabi model, anisotropic Rabi model and asymmetric Rabi model, into rotating frame, and regard them as periodically driven quantum systems. The analytical solutions of the quasi-energy spectrum as well as the Floquet modes for both models are constructed by applying the Floquet theory and the high-frequency expansion, which is applied to the non-stroboscopic dynamics of physical observables such as atomic inversion, transverse magnetization, atom-field correlation, etc. For anisotropic Rabi model, the quasi energy fits well with the numerical results even when the rotating-wave coupling is in the deep-strong coupling regime $g\simeq\hbarω$ if the counterrotating terms is small enough compared to the driving frequency. Avoided level crossing may occur for quasi energy with the same parity when the positive branch spectrum lines for the total excitation number $N$ cross the negative branch lines for $N+2$, while the high frequency expansion fails to predict this due to the conservation of the total excitation number. Furthermore, we present analytical and numerical study of the long-time evolution of population and figure out the analytical method is credible for the population dynamics. For asymmetric Rabi model, we find that the external bias field which breaks the parity symmetry of total excitation number tends to cluster the upper and lower branches into two bundles, and the detuning induced gap in the first temporal Brillouin zone shows a quadratic dependence on the bias. Both models prove that treating the Hamiltonian in the rotating frame by Floquet theory gives an alternative tool in the study of interaction between atom and light.
