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Communications in Theoretical Physics

Vibratile Coherence and Squeezing in Two Trapped Ions

Zeng Hao-Sheng, Kuang Le-Man, Xiwen Zhu, Kelin Gao

Published Mar 15, 2002• 3 citations
Publisher

Abstract

It is shown that two trapped ions interacting with laser beams resonant to the first red side-band of center-of-mass mode, in Lamb Dicke regime and under rotating wave approximation, is described by a Jaynes-Cummings model. For the initial condition that the motional state of centor-of-mass mode is in vacuum state and the internal state is prepared in a coherent superposition of states, coherence and squeezing for the vibratile motion of center-of-mass mode are discussed, particularly, a weak coherent state and a weak squeezed vacuum state are obtained. Collapse and revival are also observed in this type of initial condition.

DOI
10.1088/0253-6102/37/3/341

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It is shown that two trapped ions interacting with laser beams resonant to the first red side-band of center-of-mass mode, in Lamb Dicke regime and under rotating wave approximation, is described by a Jaynes-Cummings model. For the initial condition that the motional state of centor-of-mass mode is in vacuum state and the internal state is prepared in a coherent superposition of states, coherence and squeezing for the vibratile motion of center-of-mass mode are discussed, particularly, a weak coherent state and a weak squeezed vacuum state are obtained. Collapse and revival are also observed in this type of initial condition.
It is shown that two trapped ions interacting with laser beams resonant to the first red side-band of center-of-mass mode, in Lamb Dicke regime and under rotating wave approximation, is described by a Jaynes-Cummingsmodel. For the initial condition that the motional state of center-of-mass mode is in vacuum state and the internal stateis prepared in a coherent superposition of states, coherence and squeezing for the vibratile motion of center-of-mass modeare discussed, particularly, a weak coherent state and a weak squeezed vacuum state are obtained. Collapse andrevival are also observed in this type of initial condition.
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.
While the frequency of classical driving filed is resonant to the redside band of center-of-mass mode and without Lamb-Dicke limit,the dynamics of the internal states of two trapped ions coupled to their phonon filed can be described by a nonlinear Jaynes-Cummings model.When the internal state of trapped ions is initially in a non-coherent mixed state and the phonon field in a vacuum state,the evolved state of the phonon field does not appear squeezing;However,when the internal state is initially in a coherent superposition pure state and the phonon field in a vacuum state,the evolved state of the phonon field shows squeezing.Under proper initial conditions,the squeezing is persistent and periodic in time.