Model for Trapped Ion Interacting with Standing Wave via Gauge-Like Transformations

概要

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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 η; the extension to higher orders in η 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. The ansatz of leaving invariant the Pauli algebra after the transformations amounts to a linear transformation in the su(2) algebra describing the two level system. The outcome is a Jaynes-Cummings like Hamiltonian with effective coupling dependent on the parameter χ aimed to figure the trapping location in the standing wave. The main idea, namely leaving the Hamiltonian from invariant while changing the physical parameters can pave the way to a new understanding of gauge like transformations in the present context.
理論物理学刊行会の論文
1998-04-25