Unified Solution Formulas to Jaynes-Cummings Models with Field Nonlinearity and Strong Atom-Field Coupling

Unified and standardized solving formulas for eigenvalues, eigenvectors, evolution operators, time-varying atomic inversion and photon numbers are given to single-mode Jaynes-Cummings models with any forms of intensity-dependent atom-field coupling and the nonlinearity of the quantized photonic field itself such as the Kerr effect.