Trapped-Ion Quantum Simulator: Experimental Application to Nonlinear Interferometers

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-[Formula presented] particle in an external potential. This system is also able to simulate other physical dynamics. As a demonstration, we simulate the action of two [Formula presented] order nonlinear optical beam splitters comprising an interferometer sensitive to phase shift in one of the interferometer beam paths. The sensitivity in determining these phase shifts increases linearly with [Formula presented], and the simulation demonstrates that the use of nonlinear beam splitters ([Formula presented]) enhances this sensitivity compared to the standard quantum limit imposed by a linear beam splitter ([Formula presented]).