Symmetric rotating-wave approximation for the generalized single-mode spin-boson system
Symmetric rotating-wave approximation for the generalized single-mode spin-boson system
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DOI：
10.1103/physreva.84.042110
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发表时间：
2011-10-11
影响因子：
2.9
通讯作者：
Brumer, Paul
中科院分区：
文献类型：
--
作者：
Albert, Victor V.;Scholes, Gregory D.;Brumer, Paul
单模自旋玻色子模型表现出超强和深强耦合状态下旋转波近似 (RWA) 中未包含的行为，其中反向旋转贡献变得很重要。我们引入了一种对称旋转波近似，它同等地对待旋转和反向旋转项，保留哈密顿量相对于其参数的不变性，并再现自旋玻色子谱的几个定性特征，这些特征在非共振和深强耦合下的原始旋转波近似中不存在。对称旋转波近似允许处理某些超强和深强耦合状态，其精度和数学简单性与弱耦合状态下的 RWA 相似。此外，我们对旋转波近似的广义形式进行对称化，以获得相同的定性对应关系，并增加与精确数值结果的改进的定量一致性。如果需要，该方法很容易扩展到更高的精度。最后，我们引入了双光子拉比哈密顿量的双光子奇偶算子，并得到了其广义对称旋转波近似。该算子的存在揭示了与拉比哈密顿量类似的奇偶对称性，以及双光子情况特有的另一种对称性，提供了对双光子光谱的数学结构的深入了解，显着简化了数值，并揭示了一些有趣的动力学性质。
The single-mode spin-boson model exhibits behavior not included in the rotating-wave approximation (RWA) in the ultra and deep-strong coupling regimes, where counter-rotating contributions become important. We introduce a symmetric rotating-wave approximation that treats rotating and counter-rotating terms equally, preserves the invariances of the Hamiltonian with respect to its parameters, and reproduces several qualitative features of the spin-boson spectrum not present in the original rotating-wave approximation both off-resonance and at deep-strong coupling. The symmetric rotating-wave approximation allows for the treatment of certain ultra-and deep-strong coupling regimes with similar accuracy and mathematical simplicity as does the RWA in the weak-coupling regime. Additionally, we symmetrize the generalized form of the rotating-wave approximation to obtain the same qualitative correspondence with the addition of improved quantitative agreement with the exact numerical results. The method is readily extended to higher accuracy if needed. Finally, we introduce the two-photon parity operator for the two-photon Rabi Hamiltonian and obtain its generalized symmetric rotating-wave approximation. The existence of this operator reveals a parity symmetry similar to that in the Rabi Hamiltonian as well as another symmetry that is unique to the two-photon case, providing insight into the mathematical structure of the two-photon spectrum, significantly simplifying the numerics, and revealing some interesting dynamical properties.