{
  "id": "1501.06637",
  "version": "v1",
  "published": "2015-01-27T01:38:08.000Z",
  "updated": "2015-01-27T01:38:08.000Z",
  "title": "Algebraic structure of the two-qubit quantum Rabi model and its solvability using Bogoliubov operators",
  "authors": [
    "Jie Peng",
    "Zhongzhou Ren",
    "Haitao Yang",
    "Guangjie Guo",
    "Xin Zhang",
    "Guoxing Ju",
    "Xiaoyong Guo",
    "Chaosheng Deng",
    "Guolin Hao"
  ],
  "categories": [
    "quant-ph"
  ],
  "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 \\hbar\\omega, 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 $E=N\\hbar\\omega$ (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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-01-27T01:38:08.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "algebraic structure",
      "bogoliubov operators",
      "infinite-dimensional two-qubit quantum rabi hamiltonian",
      "general two-qubit quantum rabi model",
      "solvability"
    ],
    "publication": {
      "doi": "10.1088/1751-8113/48/28/285301",
      "journal": "Journal of Physics A Mathematical General",
      "year": 2015,
      "month": "Jul",
      "volume": 48,
      "number": 28,
      "pages": 285301
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015JPhA...48B5301P"
    }
  }
}