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Chin. Phys. B, 2018, Vol. 27(5): 054219    DOI: 10.1088/1674-1056/27/5/054219
ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID DYNAMICS Prev   Next  

An analytical variational method for the biased quantum Rabi model in the ultra-strong coupling regime

Bin-Bin Mao(毛斌斌)1, Maoxin Liu(刘卯鑫)2, Wei Wu(吴威)2, Liangsheng Li(李粮生)3, Zu-Jian Ying(应祖建)4, Hong-Gang Luo(罗洪刚)1,2
1 Center of Interdisciplinary Studies & Key Laboratory for Magnetism and Magnetic Materials of the Ministry of Education, Lanzhou University, Lanzhou 730000, China;
2 Beijing Computational Science Research Center, Beijing 100193, China;
3 Science and Technology on Electromagnetic Scattering Laboratory, Beijing 100854, China;
4 CNR-SPIN, I-84084 Fisciano(Salerno), Italy and Dipartimento di Fisica "E. R. Caianiello," Universito di Salerno, I-84084 Fisciano(Salerno), Italy
Abstract  

An analytical variational method for the ground state of the biased quantum Rabi model in the ultra-strong coupling regime is presented. This analytical variational method can be obtained by a unitary transformation or alternatively by assuming the form of the ground state wave function. The key of the method is to introduce a variational parameter λ, which can be determined by minimizing the energy functional. Using this method, we calculate the physical observables with high accuracy in comparison with the numerical exact ones. Our method evidently improves over the widely used general rotating-wave approximation (GRWA) in both qualitative and quantitative aspects.

Keywords:  ultra-strong coupling      biased quantum Rabi model      analytical variational method  
Received:  17 December 2017      Revised:  19 February 2018      Published:  05 May 2018
PACS:  42.50.Pq (Cavity quantum electrodynamics; micromasers)  
  42.50.Hz (Strong-field excitation of optical transitions in quantum systems; multiphoton processes; dynamic Stark shift)  
  03.65.Ge (Solutions of wave equations: bound states)  
Fund: 

Project supported by the National Natural Science Foundation of China (Grant Nos.11674139,11604009,and 11704025),the Program for Changjiang Scholars and Innovative Research Team in University,China (Grant No.IRT-16R35),and the Fundamental Research Funds for the Central Universities,China.ZJY also acknowledges the financial support of the Future and Emerging Technologies (FET) programme within the Seventh Framework Programme for Research of the European Commission,under FET-Open Grant No.618083(CNTQC).

Corresponding Authors:  Hong-Gang Luo     E-mail:  luohg@lzu.edu.cn

Cite this article: 

Bin-Bin Mao(毛斌斌), Maoxin Liu(刘卯鑫), Wei Wu(吴威), Liangsheng Li(李粮生), Zu-Jian Ying(应祖建), Hong-Gang Luo(罗洪刚) An analytical variational method for the biased quantum Rabi model in the ultra-strong coupling regime 2018 Chin. Phys. B 27 054219

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