  We show how an experimentally realized set of operations on a single trapped
ion is sufficient to simulate a wide class of Hamiltonians of a spin-1/2
particle in an external potential. This system is also able to simulate other
physical dynamics. As a demonstration, we simulate the action of an $n$-th
order nonlinear optical beamsplitter. Two of these beamsplitters can be used to
construct an interferometer sensitive to phase shifts in one of the
interferometer beam paths. The sensitivity in determining these phase shifts
increases linearly with $n$, and the simulation demonstrates that the use of
nonlinear beamsplitters ($n$=2,3) enhances this sensitivity compared to the
standard quantum limit imposed by a linear beamsplitter ($n$=1).
