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Chinese Physics

Micro-motion effect of a trapped ultra-cold ion in a standing-wave laser

Jiang Yurong, Feng Mang, Gao Ke-kin, Zhu Xi-wen

Published Mar 1, 2001• 3 citations
Publisher

Abstract

In the absence of the requirements of the Lamb-Dicke limit and rotating wave approximation, we semi-classically investigate the dynamics of a trapped ultra-cold ion in the standing-wave laser, with the consideration of the time-dependent potential and pseudo-potential of the Paul trap. The specific calculations show that the larger the Lamb-Dicke parameter η and the Rabi frequency Ω, the greater the difference between the dynamics in the time-dependent potential and the pseudo-potential.

DOI
10.1088/1009-1963/10/3/306

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In the absence of the requirements of the Lamb-Dicke limit and rotating wave approximation, we semi-classically investigate the dynamics of a trapped ultra-cold ion in the standing-wave laser, with the consideration of the time-dependent potential and pseudo-potential of the Paul trap. The specific calculations show that the larger the Lamb-Dicke parameter η and the Rabi frequency Ω, the greater the difference between the dynamics in the time-dependent potential and the pseudo-potential.
An ultracold two-level ion experiencing the standing wave of a resonant laser in a Paul trap is investigated in the Lamb-Dicke limit and weak excitation regime, with full consideration of the time-dependence of the trapping potential. The analytical forms of the wave functions of the system can be described with our approach, and the time evolution of the pseudo-energy of the system as well as the squeezing property of the quadrature components is studied in comparison with the treatment of harmonic oscillator model.
For the case of standing wave laser field, we investigate the internal dynamics of a Paul-trapped ion for different cases of the micromotion frequency by means of nonlinear Jaynes–Cummings model and compare our model with the pseudopotential model. The specific calculations show that, when values of dc and ac voltages are fixed, the larger the micromotion frequency is, the smaller the difference between the two models becomes and the larger the Rabi frequency is, for both within and beyond the Lamb–Dicke regime. Moreover, the property of the trapped ion staying whether on the node or on the antinode of the standing wave field is first presented.
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.
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.