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理论物理通讯：英文版

Transition Probabilities Among Fock States of an Ion in Harmonic Trap due to Alternating Electric Field

Wu ., Ying, Yang Yang, Xiao-Xue

Published Jan 1, 2002• 0 citations
OpenAlex

Abstract

In this paper, we derive the exact analytical expressions of the transition probabilities among the Fock states of an ion in a harmonic trap due to the presence of an alternating electric field.

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The transitions between stationary states in multilevel quantum system under the influence of an alternating external electric field are considered in this work. Herewith the strength of external electric field changes with time by the harmonic law. The analytical expressions for quantum transitions probabilities of a system are given at the third order of perturbation theory. The dependencies of quantum transitions probabilities and average energy of a system upon interaction time and frequency of field are investigated in the case when the system is a charged particle in rectangular infinitely deep potential pit.
We present an alternative scheme to exactly implement one-qubit and two-qubit quantum gates with a single trapped cold ion driven by a travelling laser field. The internal degree of freedom of the ion acts as the target qubit and the control qubit is encoded by two Fock states of the external vibration of the ion. The conditions to realize these operations, including the duration of each applied laser pulse and Lamb-Dicke parameter, are derived. In our scheme neither the auxiliary atomic level nor the Lamb-Dicke approximation is required. The multiquantum transition between the internal and external degrees of freedom of the ion is considered.