The quantum Rabi model (QRM) describes the interaction between a two-level system (qubit) and a quantum harmonic oscillator. In the limit where the qubit frequency is smaller than the harmonic frequency, the QRM can be well approximated by the adiabatic approximation (AA). The AA is widely used due to its simplicity and explicit physical interpretation. However, the level crossings in the spectrum of the QRM predicted by the AA are determined by the zeros of Laguerre polynomials, which deviate from the exact points. We propose an approximation to the QRM that predicts the level crossings correctly. This is done by exploiting a surprising connection between isolated exact solutions to the QRM and the Laguerre polynomials in the AA. We thus refer to this approach as the generalized adiabatic approximation (GAA). By construction, the GAA always predicts the exact exceptional spectrum and approximates the regular spectrum remarkably well in a much larger parameter regime than the AA. This generalized approach offers a framework to deal with the family of Rabi-type light-matter interaction models in a simple but accurate manner.

中文翻译：

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量子 Rabi 模型的广义绝热近似

量子 Rabi 模型 (QRM) 描述了两级​​系统 (qubit) 和量子谐振子之间的相互作用。在量子位频率小于谐波频率的极限下，QRM 可以通过绝热近似 (AA) 很好地近似。AA 因其简单和明确的物理解释而被广泛使用。然而，由 AA 预测的 QRM 频谱中的水平交叉点由 Laguerre 多项式的零点决定，这些零点偏离了精确点。我们提出了 QRM 的近似值，可以正确预测平交道口。这是通过利用 QRM 的孤立精确解与 AA 中的 Laguerre 多项式之间的惊人联系来完成的。因此，我们将这种方法称为广义绝热近似 (GAA)。通过建设，在比 AA 大得多的参数范围内，GAA 总是能准确预测异常谱并非常好地近似正则谱。这种通用方法提供了一个框架，可以以简单但准确的方式处理 Rabi 型光-物质相互作用模型系列。