  We derive an explicit formula for an entanglement measure of mixed quantum
states in a multi-level atom interacting with a cavity field within the
framework of the quantum mutual entropy. We describe its theoretical basis and
discuss its practical relevance (especially in comparison with already known
pure state results). The effect of the number of levels involved on the
entanglement is demonstrated via examples of three-, four- and five-level atom.
Numerical calculations under current experimental conditions are performed and
it is found that the number of levels present changes the general features of
entanglement dramatically.
