  Distribution of the entangled state of trapped atomic ions to long distance
using quantum repeater protocol is considered. Indeed, the long distance is
divided into short parts, and then using entanglement generation and
entanglement swapping techniques in optomechanical cavities, the entanglement
is distributed. To do the task, we perform interaction between trapped atomic
ions in optomechanical cavities, operate proper measurements on trapped ions
and also make Bell state measurement as a well-known way to swap the
entanglement. Accordingly, the entanglement is distributed between target ions
with satisfactory values of success probability and entanglement degree. The
effects of detuning and amplitude of pump laser on the entanglement and success
probability are evaluated. The uctuations of entanglement and success
probability are decreased by increasing of detuning. Via increasing the
amplitude of pump laser, the maxima of entanglement are repeated more times and
success probability undergoes the collapse-revival phenomenon.
