Proposal for measurement of harmonic oscillator berry phase in ion traps

We propose a scheme for measuring the Berry phase in the Vibrational degree of freedom of a trapped ion. Starting from the ion in a Vibrational cohere nt state we show how to reverse the sign of the coherent state amplitude by using a purely geometric phase. This can then be detected through the inte rnal degrees of freedom of the ion. Our method can be applied to preparatio n of entangled states of the ion and the vibrational mode.