Thermal properties of trapped ions: A Green’s-function method

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Abstract
We analyzed the influence of the thermal motion from the environment on the internal states of trapped ions and the center-of-mass mode phonon using a Green’s-function method. The deviation of the internal states and the variational rules of the phonon number with different trap parameters changing with the temperature are given. The upper limit of the temperature at which the gate operation can be performed safely is convenient to be found out according to different error correction capability.