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Communications in Theoretical Physics

Continued Fraction Approach to the Solution of a Trapped Ultracold Ion Interacting with a Standing Wave Laser without Rotating Wave Approximation

Feng Mang, Zhu XiWen, Yong Li, Shi Lei, Gao KeLin

Published Oct 30, 2000• 0 citations
Publisher

Abstract

In coherent state representation and in the absence of rotating wave approximation, we present an approach to solve the interaction of a trapped ultracold ion with a standing wave laser by a continued fraction, within the Lamb–Dicke limit and the low excitation regime. It is shown that, the eigen-energies as well as the coefficients of the series of the eigenfunction can be obtained rapidly from the continued fraction.

DOI
10.1088/0253-6102/34/3/385

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In coherent state representation and in the absence of rotating wave approximation, we present an approach to solve the interaction of a trapped ultracold ion with a standing wave laser by a continued fraction, within the Lamb–Dicke limit and the low excitation regime. It is shown that, the eigen-energies as well as the coefficients of the series of the eigenfunction can be obtained rapidly from the continued fraction.
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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.