Validity of Lamb-Dicke Approximations in Ion-Trap Systems

• Published in: Chinese physics letters Vol. 27; no. 1; pp. 21 - 24
• Main Author: 蓝海江 张淼 韦联福
• Format: Journal Article
• Language: English
• Published: IOP Publishing 2010
• Subjects: Approximation; CNOT门; Dynamical systems; Dynamics; Gates; LDA; Mathematical analysis; 保真度; 离子阱; 量子动力学
• ISSN: 0256-307X; 1741-3540
• DOI: 10.1088/0256-307X/27/1/010304

The Lamb-Dicke （LD） approximation （LDA） is usually utilized to simplify the treatments for the dynamics of ion-trap systems, where the so-called LD parameters should be sufficiently small. In this Letter, based on the quantum dynamics of a single trapped ion beyond the LDA, we discuss the fidelities of the control-NOT （CNOT） gate generated by performing the usual LDA. It is shown that the fidelity of the generated CNOT gate under the LDA is sufficiently high for the current LD experiments, e.g., it reaches 99.9% for η=0.20. The validity of the LDA is also discussed by calculating these fidelities for slightly larger LD parameters, e.g., η=0.4, etc.