Peng, J (reprint author), Xiangtan Univ, Lab Quantum Engn & Micronano Energy Technol, Xiangtan 411105, Hunan, Peoples R China.
We have found the algebraic structure of the two-qubit quantum Rabi model behind the possibility of its novel exceptional eigenstates with finite photon numbers by analyzing the Hamiltonian in the photon number space. The exceptional solutions with at most 1 photon exist in the whole qubit-photon coupling regime with constant eigenenergy equal to single photon energy h omega, which can be clearly demonstrated from the Hamiltonian structure. With a similar method, we find that these special dark-state-like eigenstates (the eigenenergy is coupling-independent, but the wave function is coupling-dependent) commonly exist for the two-qubit Jaynes-Cummings model, with E = Nh omega (N = -1, 0, 1,...), and one of them is also the eigenstate of the two-qubit quantum Rabi model, which is interesting for application in a simpler way. Besides, using Bogoliubov operators, we analytically retrieve the solution of the general two-qubit quantum Rabi model. In this concise and physical way, we clearly see how the eigenvalues of the infinite-dimensional two-qubit quantum Rabi Hamiltonian are determined by a convergent power series, so that the solution can reach arbitrary accuracy conveniently because of the convergence property.
National Natural Science Foundation of China [11347112, 11204263, 11035001, 11404274, 10735010, 10975072, 11375086, 11120101005]
; 973 National Major State Basic Research and Development of China [2010CB327803, 2013CB834400]
; CAS Knowledge Innovation Project [KJCX2-SW-N02]
; Research Fund of Doctoral Point (RFDP) Grant 
; Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD)
; Scientific Research Fund of Hunan Provincial Education Department [12C0416]
; Program for Changjiang Scholars and Innovative Research Team in University [IRT13093]
Peng, J,Ren, ZZ,Yang, HT,et al. Algebraic structure of the two-qubit quantum Rabi model and its solvability using Bogoliubov operators[J]. JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL,2015,48(28):285301.