 For deriving the JCM interaction Hamiltonian the quantized radiation field is taken to consist of a single bosonic mode with the field operator
formula_8, where the operators formula_9 and formula_10 are the bosonic creation and annihilation operators and formula_11 is the angular frequency of the mode.On the other hand, the two-level atom is equivalent to a spin-half whose state can be described using a three-dimensional Bloch vector.