  Recent experiments [K. R. Brown, et al., Nature 471, 196 (2011); and M.
Harlander, et al., Nature 471, 200 (2011)] have demonstrated the coherent
manipulations on the external vibrations of two ions, confined individually in
the separated ion traps. Using these recently developed techniques, we propose
here an approach to realize the coherent operations, e.g., the universal
quantum gates, between the separated ion-trap qubits encoded by two internal
atomic states of the trapped ions. Our proposal operates beyond the usual
Lamb-Dicke limits, and could be applied to the scalable ion traps coupled by
their vibrations.
