  We investigate the non-dissipative decoherence of three qubit system obtained
by manipulating the state of a trapped two-level ion coupled to an optical
cavity. Modelling the environment as a set of noninteracting harmonic
oscillators, analytical expressions for the state operator of tripartite
composite system, the probability of generating maximally entangled GHZ state,
and the population inversion have been obtained. The pointer observable is the
energy of the isolated quantum system. Coupling to environment results in
exponential decay of off diagonal matrix elements of the state operator with
time as well as a phase decoherence of the component states.
  Numerical calculations to examine the time evolution of GHZ state generation
probability and population inversion for different system environment coupling
strengths are performed. Using negativity as an entanglement measure and linear
entropy as a measure of mixedness, the entanglement dynamics of the tripartite
system in the presence of decoherence is analysed.
