Exact solutions to the Jaynes-Cummings model without the rotating-wave approximation

¹ Center for Statistical Theoretical Condensed Matter Physics, Zhejiang Normal University - Jinhua 321004, PRC
² Department of Physics, Zhejiang University - Hangzhou 310027, PRC
³ Department of Physics, Southwest University of Science and Technology - Mianyang 621010, PRC
⁴ Center for Modern Physics, Chongqing University - Congqing 400044, PRC
⁵ Department of Modern Physics, University of Science and Technology of China - Hefei 230026, PRC

^a qhchen@zju.edu.cn

Received: 5 June 2011
Accepted: 17 August 2011

Abstract

By using tunable extended bosonic coherent states, the JC model without the rotating-wave approximation can be mapped to a polynomial equation with a single variable. The solutions to this polynomial equation recover exactly all eigenvalues and eigenfunctions of the model for all coupling strengths and detunings, which can be readily applied to recent circuit quantum electrodynamic systems operating in the ultra-strong coupling regime.