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理论物理通讯：英文版

Simple Approach to the Solution of a Trapped and Radiated Cold Ion Beyond the Lamb—Dicke Limit

FENGMang, Shilei

Published Jan 1, 2002• 0 citations
OpenAlex

Abstract

Trapping ions outside the Lamb-Dicke limit have been proven to be useful for the laser-cooling and quantum computing.Under the supposition of the Rabi frequency much smaller than the Lamb Dicke parameter,we can use a simple method to analytically solve the system with a single cold ion trapped and radiated beyond the Lamb Dickc limit,in the absence of the rotating-wave approximation (RWA).Discussion has been made for the limitation of our approach and the comparison of our results with the solutions under the RWA.

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Trapping ions outside the Lamb-Dicke limit have been proven to be useful for the laser-cooling and quantum computing.Under the supposition of the Rabi frequency much smaller than the Lamb Dicke parameter,we can use a simple method to analytically solve the system with a single cold ion trapped and radiated beyond the Lamb Dickc limit,in the absence of the rotating-wave approximation (RWA).Discussion has been made for the limitation of our approach and the comparison of our results with the solutions under the RWA.
Trapping ions outside the Lamb–Dicke limit have been proven to be useful for the laser-cooling and quantum computing. Under the supposition of the Rabi frequency much smaller than the Lamb–Dicke parameter, we can use a simple method to analytically solve the system with a single cold ion trapped and radiated beyond the Lamb– Dicke limit, in the absence of the rotating-wave approximation (RWA). Discussion has been made for the limitation of our approach and the comparison of our results with the solutions under the RWA.
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.
We study laser cooling of two ions that are trapped in a harmonic potential and interact by Coulomb repulsion. Sideband cooling in the Lamb-Dicke regime is shown to work analogously to sideband cooling of a single ion. Outside the Lamb-Dicke regime, the incommensurable frequencies of the two vibrational modes result in a quasicontinuous energy spectrum that significantly alters the cooling dynamics. The cooling time decreases nonlinearly with the linewidth of the cooling transition, and the effect of dark states which may slow down the cooling is considerably reduced. We show that cooling to the ground state is also possible outside the Lamb-Dicke regime. We develop the model and use quantum Monte Carlo calculations for specific examples. We show that a rate equation treatment is a good approximation in all cases.