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Communications in Theoretical Physics

Series Solution of a Trapped Ultracold Ion in a Raman-Type Configuration

Feng Mang, Xiwen Zhu, Kelin Gao, Shi Lei

Published Aug 15, 2001• 0 citations
Publisher

Abstract

The Raman interaction of a trapped ultracold ion with two traveling wave lasers is studied analytically by series expansion technique without the need of rotating wave approximation and the limitations of both the Lamb–Dicke limit and the weak excitation regime. As an example, a scheme for the preparation of Schrödinger-cat states in such a process is proposed beyond the weak excitation regime.

DOI
10.1088/0253-6102/36/2/207

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Communications in Theoretical Physics•Oct 30, 2000•0 citations
The Raman interaction of a trapped ultracold ion with two traveling wave lasers is studied analytically by series expansion technique without the need of rotating wave approximation and the limitations of both the Lamb–Dicke limit and the weak excitation regime. As an example, a scheme for the preparation of Schrödinger-cat states in such a process is proposed beyond the weak excitation regime.
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.
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.
By means of the Bloch–Maxwell equation, the Raman interaction of a trapped ultracold ion with two traveling wave lasers is treated semiclassically. As the model works without limitation of the Lamb–Dicke limit and the weak excitation regime, we study chaotic behavior of the system in the wide range of the parameters. It is shown that the chaotic behavior is more and more pronounced with the increase of the Lamb–Dicke parameter and Rabi frequency, and can be exhibited experimentally by using quantum jump technique.
By means of the Bloch-Maxwell equation, the Raman interaction of a trapped ultracold ion with two traveling wave lasers is treated semiclassically. As the modcl works without limitation of the Lamb-Dicke limit and the weak excitation regime, we study chaotic behavior of the system in the wide range of the parameters. It is shown that the chaotic behavior is more and more pronounced with the increase of the Lamb-Dicke parameter and Rabi frequency,and can be exhibited experimentally by using quantum jump technique.``