Model for Trapped Ion interacting with Standing Wave

Abstract

We treat the interaction of a trapped ion with a standing-wave light field relaxing the previous condition of the trapping ion being on the node of the standing wave. In addition we work to second order in the Lamb-Dicke parameter $\eta$, the extension to higher orders in $\eta$ is also indicated. Only a simple transformation to the ``dressed basis'' [subject to the constraint of Pauli algebra] is required in order to show that the ion interacting with a standing light-wave may be described by the Jaynes-Cummings Hamiltonian.