Geometric phase for two trapped ions

Summary form only given. First we explore how to perform single trit rotations, so that we can (in principle) prepare any pure trit state at will and move it around in the pure stare manifold. Pure stares of three level systems can be represented in terms of the five dimensional manifold of the coset space SU(3)/U(2). These trit rotations have to consist of the laser pulse techniques developed for ion traps. We show how, using those techniques, we can move the state around a closed path in Hilbert space.