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arXiv · 1305.6782

Analytical eigenstates for the quantum Rabi model

Honghua Zhong·Qiongtao Xie·Murray Batchelor·Chaohong Lee
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Abstract

We develop a method to find analytical solutions for the eigenstates of the quantum Rabi model. These include symmetric, anti-symmetric and asymmetric analytic solutions given in terms of the confluent Heun functions. Both regular and exceptional solutions are given in a unified form. In addition, the analytic conditions for determining the energy spectrum are obtained. Our results show that conditions proposed by Braak [Phys. Rev. Lett. \textbf{107}, 100401 (2011)] are a type of sufficiency condition for determining the regular solutions. The well-known Judd isolated exact solutions appear naturally as truncations of the confluent Heun functions.

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Honghua Zhong, Qiongtao Xie, Murray Batchelor, Chaohong Lee. 2013-05-29. Analytical eigenstates for the quantum Rabi model. https://doi.org/10.1088/1751-8113/46/41/415302

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