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The Journal of Atomic and Molecular Sciences

Entanglement Dynamics of Two Trapped Ions in the Intermediate Excitation Regime

Zhong-Jie Wang, C. Y. Fan

Published Jan 1, 2010• 0 citations
Publisher

Abstract

We have studied the model for interaction of two trapped ions in a trap with a laser beam in the intermediate excitation regime. By applying unitary transformations, the system can be transformed into the Tavis-Cummings model. The entanglement dynamics of two trapped ions in this system has been investigated. With computation of the concurrence, unlike that in Tavis-Cummings model, we find that the entanglement of two ions in our model undergoes periodic death and revivals.

DOI
10.4208/jams.030410.032810a

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We showed that in Lamb-Dicke regime and under rotating wave approximation, the dynamical behavior of two trapped ions interacting with a laser beam resonant to the first red side-band of center-of-mass mode can be described by Jaynes-Cummings Model. An exact analytic solution for this kind of Jaynes-Cummings model is presented. The results showed that quantum collapses and revivals for the occupation of two atoms, and squeezing for vibratic motion of center-of-mass mode existed in both two different types of initial conditions. The maximum momentum squeezing for center-of-mass mode in these two types of conditions are found to be 42.4% and 43.8% respectively. The coherence, in the first type of initial conditions can keeps long times, and in the second type of initial conditions, a concrete form of coherent state is obtained, when the initial average number is very small.
The nonlinear interaction of three ions in a linear trap with laser light is studied by taking into account the three vibrational modes within a rotating-wave approximation. It is demonstrated that, for localization conditions far from the Lamb-Dicke limit, all three modes have a significant impact on the dynamics of the system. Preparations of vibrational Fock states can be used to realize two different regimes with an exactly solvable three-atom dynamics. The first one corresponds to a nonlinear version of the Tavis-Cummings coupling, whereas the Tavis-Cummings type interactions are suppressed in the second one.