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

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. Copyright (C) EPLA, 2011