  In this paper, a model by which we study the interaction between a motional
three-level atom and two-mode field injected simultaneously in a bichromatic
cavity is considered; the three-level atom is assumed to be in a $\Lambda$-type
configuration. As a result, the atom-field and the field-field interaction
(parametric down conversion) will be appeared. It is shown that, by applying a
canonical transformation, the introduced model can be reduced to a well-known
form of the generalized Jaynes-Cummings model. Under particular initial
conditions, which may be prepared for the atom and the field, the time
evolution of state vector of the entire system is analytically evaluated. Then,
the dynamics of atom by considering `atomic population inversion' and two
different measures of entanglement, i.e., `von Neumann entropy' and
`idempotency defect' is discussed, in detail. It is deduced from the numerical
results that, the duration and the maximum amount of the considered physical
quantities can be suitably tuned by selecting the proper field-mode structure
parameter $p$ and the detuning parameters.
