Solution of a Multiatom Radiation Model Using the Bargmann Realization of the Radiation Field

A model for interacting single-mode electromagnetic radiation and matter consisting of $N$ two-level particles is solved exactly using a representation in which the creation and destruction operators for the field act by multiplication and differentiation, respectively. The model includes off-resonant interactions. Closed-form expressions can be given for some special cases. The solutions are transformed to the more familiar Fock and Schrödinger representations. Numerical results are given to indicate the behavior of the solutions. An equation for a generating function is derived which would give solutions of the (algebraic) matrix equation to which the problem has been reduced.