Atoms in fock state fields: I. Exact analytical results

Abstract

A theoretical analysis of the fundamental problem of two-level atomic systems radiatively decaying and coupled to Fock state radiation fields is presented. First, for a broad-band Fock state field and for a single two-level atom the Einstein radiation rate equation is derived within a scheme of matter-field statistical decorrelation. This holds too for N > 1 “independent” two-level atoms. Second, for a single-mode Fock state field exact analytical solution for the atomic inversion, in the single-atom case, is derived within the rotating wave approximation. For N > 1 cooperative two-level atoms exact results are also derived in the steady state regime. In a thermodynamic limit where N→ ∞, the scaled atomic inversion is expressed as Poisson-Charlier polynomials. Connection with earlier results for coherent and incoherent (chaotic) state fields is made. Of mathematical interest: a formal expression for the cofactor elements in terms of the original elements of a triangular matrix is derived in appendix B.