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Chinese journal of atomic and molecular physics

Dynamics of the interaction between a trapped ultracold ion and a standing wave laser without rotating wave approximation

Jiang Yu

Published Jan 1, 2000• 0 citations
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Abstract

In an interaction representation, we study the dynamics of the interaction between a trapped ultracold ion and a standing wave laser within the Lanb Dicke limit. As the rotating wave approximation is not introduced the ions motion becomes more and more chaotic with the increase of the Lamb Dicke parameter and Rabi frequency. Finally, we make a comparison of our results with those under the rotating wave approximation.

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In an interaction representation, we study the dynamics of the interaction between a trapped ultracold ion and a standing wave laser within the Lanb Dicke limit. As the rotating wave approximation is not introduced the ions motion becomes more and more chaotic with the increase of the Lamb Dicke parameter and Rabi frequency. Finally, we make a comparison of our results with those under the rotating wave approximation.
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.``
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.