Abstract
Two non-interacting trapped-ions, with intrinsic decoherence, are located in two sets of spatially separated cavities. The quantum correlations, of the two noninteracting ion's internal electronic states, are investigated by using geometric quantum discord (GQD), measurement-induced nonlocality (MIN) and quantum entanglement (QE). The influence of both the intrinsic decoherence and mean photon number on the correlations, with resonant or off-resonant case, is discussed. The correlations appear periodically when intrinsic decoherence is neglected, however, the intrinsic decoherence causes the decay of correlations. Its increase leads to quick disappear for the correlations. It is found that Bell violation and GQD, MIN and QE do not satisfy the monotonous relation. Also, GQD and MIN are more robust than QE under the phase decoherence, but they can be decreased by adjusting the detuning.