Spectral Degeneracies in the Asymmetric Quantum Rabi Model
Spectral Degeneracies in the Asymmetric Quantum Rabi Model
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DOI：
10.1007/978-981-10-5065-7_7
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发表时间：
2017
期刊：
影响因子：
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通讯作者：
Cid Reyes-Bustos;M. Wakayama
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文献类型：
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作者：
Cid Reyes-Bustos;M. Wakayama
本文的目的是研究确定非对称量子Rabi模型准精确谱的一族(所谓的约束)多项式。量子Rabi模型普遍存在于各种量子系统中，其潜在的应用包括量子计算和量子密码学。在Wakayama，对称性的非对称量子Rabi模型[30]中，利用李代数的表示理论，我们给出了一个等价于合流Heun常微分方程组的非对称量子Rabi模型的图景。利用这种描述，我们通过研究约束多项式，证明了对称破缺参数相等时，非对称量子Rabi模型的谱简并(谱图中的能级交叉)的存在性，并猜想出一般情况下保证能级交叉存在的公式。这些关于能级交叉的结果推广了关于简并谱的一个结果，该结果由Kuś于1985年首次针对(对称)量子拉比模型给出。2015年，Li和Batchelor对(Braak，Phys)更早的一项经验观察进行了数值演示。莱特牧师。100401-100404,2011年)[3]。在本文中，虽然没有得到猜想的证明，但我们深化了这一猜想，并给出了目标约束多项式的新公式和见解。
The aim of this article is to investigate certain family of (so-called constraint) polynomials which determine the quasi-exact spectrum of the asymmetric quantum Rabi model. The quantum Rabi model appears ubiquitously in various quantum systems and its potential applications include quantum computing and quantum cryptography. In (Wakayama, Symmetry of Asymmetric Quantum Rabi Models) [30], using the representation theory of the Lie algebra, we presented a picture of the asymmetric quantum Rabi model equivalent to the one drawn by confluent Heun ordinary differential equations. Using this description, we proved the existence of spectral degeneracies (level crossings in the spectral graph) of the asymmetric quantum Rabi model when the symmetry-breaking parameterequalsby studying the constraint polynomials, and conjectured a formula that ensures the presence of level crossings for general. These results on level crossings generalize a result on the degenerate spectrum, given first by Kuś in 1985 for the (symmetric) quantum Rabi model. It was demonstrated numerically by Li and Batchelor in 2015, investigating an earlier empirical observation by (Braak, Phys. Rev. Lett. 107, 100401–100404, 2011) [3]. In this paper, although the proof of the conjecture has not been obtained, we deepen this conjecture and give insights together with new formulas for the target constraint polynomials.