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理论物理通讯：英文版

Analytical Solution for an Ultracold Trapped Ion at the Node of the Standing Wave Laser Without Rotating Wave Approximation

Fang, Ximing, Feng, Mang

Published Jan 1, 2001• 0 citations
OpenAlex

Abstract

A method of solving an ultracold trapped ion at the node of the standing wave laser without rotating wave approximation is proposed and the analytical forms of the eigenfunctions and eigenenergies of the system are presented.

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Analytical Solution for an Ultracold Trapped Ion at the Node of the Standing Wave Laser Without Rotating Wave Approximation

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Raman interaction of a trapped ultracold ion with two travelling wave lasers has been used extensively in ion-trap experiments. We solve this interaction in the absence of a rotating wave approximation (RWA) by a continued fraction, without considering the restriction of the Lamb-Dicke limit and the weak excitation regime. Some interesting characteristics of the ion-trap system, particularly for the ion outside the weak excitation regime are found. Finally, a comparison of our results with the solution under the RWA is made.

arXiv:quant-ph/0012085•Journal of Physics B Atomic Molecular and Optical Physics•Jan 26, 2001•9 citations
In coherent state representation and in the absence of rotating wave approximation, the interaction between a standing wave laser and a trapped ultracold ion within the Lamb-Dicke limit, expanded to the second-order term of the Lamb-Dicke parameter, can be solved analytically by series expansion technique. It can be seen that, for some particular detunings, the eigenenergies of the system can be exactly obtained and the eigenfunctions, presented as series forms, are a superposition of displaced Fock states and displaced squeezed states. Making use of our solution, some particular nonclassical states could be prepared.
Raman interaction of a trapped ultracold ion with two travelling wave lasers has been used extensively in ion-trap experiments. We solve this interaction in the absence of a rotating wave approximation (RWA) by a continued fraction, without considering the restriction of the Lamb-Dicke limit and the weak excitation regime. Some interesting characteristics of the ion-trap system, particularly for the ion outside the weak excitation regime are found. Finally, a comparison of our results with the solution under the RWA is made.