Analytical eigenstates for the quantum Rabi model

被引：115

作者：

Zhong, Honghua ^{[1
,2
]}

Xie, Qiongtao ^{[2
,3
]}

Batchelor, Murray T. ^{[4
,5
,6
]}

Lee, Chaohong ^{[2
]}

机构：

[1] Jishou Univ, Dept Phys, Jishou 416000, Peoples R China

[2] Sun Yat Sen Univ, State Key Lab Optoelect Mat & Technol, Sch Phys & Engn, Guangzhou 510275, Guangdong, Peoples R China

[3] Hainan Normal Univ, Sch Phys & Elect Engn, Haikou 571158, Peoples R China

[4] Chongqing Univ, Ctr Modern Phys, Chongqing 400044, Peoples R China

[5] Australian Natl Univ, Inst Math Sci, Canberra, ACT 0200, Australia

[6] Australian Natl Univ, Dept Theoret Phys, Res Sch Phys & Engn, Canberra, ACT 0200, Australia

来源：

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL | 2013年 / 46卷 / 41期

基金：

澳大利亚研究理事会;

关键词：

JAHN-TELLER; STATES; SPACE;

D O I：

10.1088/1751-8113/46/41/415302

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

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 (2011 Phys. Rev. Lett. 107 100401) 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.

引用

页数：14

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