  We study the Jaynes-Cummings interaction when initial mixed states, for the
atom or the field, are considered. The evolved mixed field density matrix is
purified to a wavefunction that describes the interaction between a quantised
field and an artificial four-level atom. This allows us to use the Araki-Lieb
inequality to calculate the field entropy from the atomic entropy. We then
generate {\it artificial} Hamiltonians that reproduce the field entropy
dynamics. We finally show that more realistic Hamiltonians may be considered by
using two entangled two-level atoms.
