Decoherence of tripartite states - a trapped ion coupled to an optical cavity

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.