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arXiv · 1501.06637

Algebraic structure of the two-qubit quantum Rabi model and its solvability using Bogoliubov operators

Jie Peng·Zhongzhou Ren·Haitao Yang·Guangjie Guo·Xin Zhang·Guoxing Ju·Xiaoyong Guo·Chaosheng Deng·Guolin Hao
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Abstract

We have found the algebraic structure of the two-qubit quantum Rabi model behind the possibility of its novel quasi-exact solutions with finite photon numbers by analyzing the Hamiltonian in the photon number space. The quasi-exact eigenstates with at most $1$ photon exist in the whole qubit-photon coupling regime with constant eigenenergy equal to single photon energy \hbarω, which can be clear demonstrated from the Hamiltonian structure. With similar method, we find these special "dark states"-like eigenstates commonly exist for the two-qubit Jaynes-Cummings model, with $E=N\hbarω$ (N=-1,0,1,...), and one of them is also the eigenstate of the two-qubit quantum Rabi model, which may provide some interesting application in a simper way. Besides, using Bogoliubov operators, we analytically retrieve the solution of the general two-qubit quantum Rabi model. In this more concise and physical way, without using Bargmann space, we clearly see how the eigenvalues of the infinite-dimensional two-qubit quantum Rabi Hamiltonian are determined by convergent power series, so that the solution can reach arbitrary accuracy reasonably because of the convergence property.

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Jie Peng, Zhongzhou Ren, Haitao Yang, Guangjie Guo, Xin Zhang, Guoxing Ju, Xiaoyong Guo, Chaosheng Deng, Guolin Hao. 2015-01-27. Algebraic structure of the two-qubit quantum Rabi model and its solvability using Bogoliubov operators. https://doi.org/10.1088/1751-8113%2F48%2F28%2F285301

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