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Communications in Theoretical Physics

The Influence of the Micromotion on the Internal Dynamics of an Ion in a Paul Trap

Fang XiMing, Feng Mang, Shi Lei, Yan Min, Gao KeLin, Zhu XiWen

Published Jul 30, 1999• 0 citations
Publisher

Abstract

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.

DOI
10.1088/0253-6102/32/1/5

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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.
Starting from the Jaynes-Cummings (J-C) model describing interaction of a trapped ion with a standing-wave laser field, we derive the interaction Hamiltonian on the nonlinear J-C model of the trapped ion excitated resonantly with 1-quantum vibrational mode. After solving the time-dependent states of this model,the entropy evolution of the ion are investigated numerically related with Lamb-Dick parameter,the position of the ion in the standing-wave laser field and the initial number of phonon. It is shown that the entropy evolution exhibit nonperiodicity vibration. With the increasing of the parameter, it will increase the frequency of the vibration,therefore the less time of disentanglement between the internal and external degrees of freedom of a trapped ion. When moving the ion from the node of the standing-wave laser to the antinode,the frequency of the vibration becomes less,the longer time of the disentanglement between the internal and external degrees of freedom. With the more initial number of phonon , the entropy evolution of the ion is similar to the field entropy evolution of Jaynes-Cummings model, and the vibration frequency become less gradually.
Laser cooling of a single trapped ion in a Paul trap is discussed theoretically in the Lamb-Dicke limit, with full consideration of the time dependence of the trapping potential. Resulting mean kinetic energies are defined as time averages over one period of the micromotion and are compared with final temperatures expected from the laser-cooling treatment with harmonic traps. For laser-atom detunings close to the micromotion frequency the results differ significantly from those expected for a harmonic trap potential. A physical interpretation is given and simple formulas are derived for the strong confinement case.
We have investigated the position-dependent dynamics of a trapped ion in a standing wave laser by transforming it to the Jaynes-Cummings-type system under the Lamb-Dicke limit. A variety of novel phenomena are exhibited, e.g. periodic collapse and revival features and long-time scaled revivals of the ionic inversion, depending on its position in the standing wave. Our result provides a way of producing a system equivalent to the two-photon Jaynes-Cummings model in the trapped ion system, with its exact periodicities.
We have investigated the position-dependent dynamics of a trapped ion in a standing wave laser by transforming it to the Jaynes-Cummings-type system under the Lamb-Dicke limit.A variety of novel phenomena are exhibited.e.g.periodic collapse and revival features and long-time scaled revivals of the ionic inversion,depending on its position in the standing wave.Our result provides a way of producing a system equivalent to the two-photon Jaynes-Cummings model in the trapped ion system,with its exact periodicities.