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arXiv 2412.20437quant-ph
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各向异性双光子量子 Rabi 模型的临界谱

Critical spectrum of the anisotropic two-photon quantum Rabi model

Jiong Li, Daniel Braak, Qing-Hu Chen

AI总结:

本文利用 Bogoliubov 算符方法研究各向异性双光子量子 Rabi 模型,推导了“谱坍缩”临界耦合处无离散谱的条件,并严格揭示了临界原子频率间束缚态数量的有限与无限分布规律,解决了该模型的所有遗留问题。

摘要:

使用 Bogoliubov 算符方法研究了各向异性双光子量子 Rabi 模型。通过解析方法确定了双重简并的例外态。通过调整属于两个相邻能级的最后一个例外点的位置,我们推导出了在发生“谱坍缩”的临界耦合处不存在离散谱的条件。在这种特殊情况下,谱在阈值能量之上变得完全连续,不存在束缚态,而一般情况下基态仍保持有能隙。这也标志着量子相变。更有趣的是,我们严格发现,在两个依赖于各向异性的临界原子频率之间存在有限个束缚态,而超出该频率范围则存在无限多个束缚态。以这种方式,双光子量子 Rabi 模型中的所有问题都得到了解决。

英文摘要:

The anisotropic two-photon quantum Rabi model is studied using the Bogoliubov operator approach. The doubly degenerate exceptional states are identified through analytical methods. By adjusting the position of the last exceptional point belonging to two adjacent energy levels, we derive a condition for the absence of the discrete spectrum at the critical coupling where ``spectral collapse" occurs. In this special case, the spectrum becomes fully continuous above a threshold energy, with no bound states existing, whereas the ground state remains gapped in the general case. This also signals a quantum phase transition. More interestingly, we rigorously find that a finite number of bound states exist between two anisotropy dependent critical atomic frequencies, with infinitely many bound states beyond this frequency regime. In this manner, all issues in the two-photon quantum Rabi model are resolved.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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