  We explore the possibility of implementing a Heisenberg-limited Mach-Zehnder
interferometry via an array of trapped ions, which obey a quantum Ising model
within a transverse field. Based upon adiabatic processes of increasing the
Ising interaction and then decreasing the transverse field, we demonstrate a
perfect transition from paramagnetism to ferromagnetic states, which can be
used as the beam splitter for the multi-ion Mach-Zehnder interferometry. The
achieved NOON state of the ions enables the Heisenberg-limited interferometry.
Using currently available techniques for ultracold ions, we discuss the
experimental feasibility of our scheme with global operations.
