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arXiv:0810.2178 · Optics Communications

Simplified approach to generate controlled-NOT gates with single trapped ions for arbitrary Lamb–Dicke parameters

Miao Zhang, Haoran Jia, L. F. Wei

Published Feb 8, 2009• 2 citations
arXivHTMLPDF
DOI
10.1016/j.optcom.2009.01.047

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Quantum controlled-NOT (CNOT) gates with single trapped cold ions have been experimentally demonstrated [C. Monroe et al., Phys. Rev. Lett. 75, 4714 (1995)] by using auxiliary atomic levels (besides the qubit ones) and under the usual Lamb-Dicke (LD) limit (wherein the so-called LD parameter, which represents the interaction strength between the internal and external degrees of freedom of the driven ion, is required to be sufficiently small). It has been shown [C. Monroe et al., Phys. Rev. A 55, R2489 (1997); L. F. Wei et al., 65, 062316 (2002)] that, beyond the LD limit, these gates could also be implemented for certain specific LD parameters. Here, we further show that, without any auxiliary atomic level, the desirable quantum logic gates could still be realized with sufficiently high fidelities for arbitrary LD parameters, as long as the durations of the applied laser pulses are accurately set within the decoherence times of the ions.

Physical Review A•Jul 30, 2008•5 citations
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.
Quantum controlled-NOT (CNOT) gates with single trapped cold ions have been experimentally demonstrated [C. Monroe et al., Phys. Rev. Lett. 75, 4714 (1995)] by using auxiliary atomic levels (besides the qubit ones) and under the usual Lamb-Dicke (LD) limit (wherein the so-called LD parameter, which represents the interaction strength between the internal and external degrees of freedom of the driven ion, is required to be sufficiently small). It has been shown [C. Monroe et al., Phys. Rev. A 55, R2489 (1997); L. F. Wei et al., 65, 062316 (2002)] that, beyond the LD limit, these gates could also be implemented for certain specific LD parameters. Here, we further show that, without any auxiliary atomic level, the desirable quantum logic gates could still be realized with sufficiently high fidelities for arbitrary LD parameters, as long as the durations of the applied laser pulses are accurately set within the decoherence times of the ions.