  The system of an atom couples to two distinct optical cavities with phase
decoherence is studied by making use of a dynamical algebraic method. We adopt
the concurrence to characterize the entanglement between atom and cavities or
between two optical cavities in the presence of the phase decoherence. It is
found that the entanglement between atom and cavities can be controlled by
adjusting the detuning parameter. Finally, we show that even if the atom is
initially prepared in a maximally mixed state, it can also entangle the two
mode cavity fields.
