English

Analytical eigenstates for the quantum Rabi model

Quantum Physics 2013-10-01 v3 Quantum Gases Atomic Physics

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.

Cite

@article{arxiv.1305.6782,
  title  = {Analytical eigenstates for the quantum Rabi model},
  author = {Honghua Zhong and Qiongtao Xie and Murray Batchelor and Chaohong Lee},
  journal= {arXiv preprint arXiv:1305.6782},
  year   = {2013}
}

Comments

15 pages, 3 figure, to appear in J. Phys. A

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