Intrinsic decoherence effects on tripartite GHZ state generation using a trapped ion coupled to an optical cavity

We analyse the effects of intrinsic decoherence on the probability of generating a tripartite GHZ state using a cool trapped ion coupled to a single mode of the cavity field and interacting with a resonant laser field. The Milburn equation is solved for this tripartite system to obtain the time evolution of the density matrix as a function of cavity-ion coupling, laser-ion coupling, and the size of the unitary time step relative to the timescale determined by system parameters. Starting with the system prepared initially in a separable state, the density matrix is used to calculate the probability of tripartite GHZ state generation using the coupling strengths reported in a recent experiment